NBER WORKING PAPER SERIES MATCHING …Matching Pennies on the Campaign Trail: An Empirical Study of...

NBER WORKING PAPER SERIES

MATCHING PENNIES ON THE CAMPAIGN TRAIL:AN EMPIRICAL STUDY OF SENATE ELECTIONS AND MEDIA COVERAGE

Camilo García-JimenoPinar Yildirim

Working Paper 23198http://www.nber.org/papers/w23198

NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts Avenue

Cambridge, MA 02138February 2017

We thank Jeff Groesback, Scott Wang, and Shawn Zamechek for excellent research assistance, and Noah Veltman for sharing with us the data on NFL fandom. We are also grateful to Daron Acemoglu, Frank DiTraglia, Gregory Martin, Maria Petrova, Carlo Prato, Noam Yuchtman, and to seminar participants at Tufts University, CEMFI, Pompeu Fabra, Stockholm University, the Wharton School, Princeton University, NYU Abu Dhabi, UC Berkeley, the Wallis Political Economy conference at the University of Rochester, the Southern Economic Association 2015 Conference, and the Stanford University SITE conference for their valuable comments. We gratefully acknowledge the financial support of the NET Institute, the Dean's Research Fund at the Wharton School, and the Hal Varian Visiting Assistant Professorship research fund at MIT. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.

NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

© 2017 by Camilo García-Jimeno and Pinar Yildirim. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.

Matching Pennies on the Campaign Trail: An Empirical Study of Senate Elections and MediaCoverageCamilo García-Jimeno and Pinar YildirimNBER Working Paper No. 23198February 2017JEL No. C50,C7,D72

ABSTRACT

We study the strategic interaction between the media and Senate candidates during elections. While the media is instrumental for candidates to communicate with voters, candidates and media outlets have conflicting preferences over the contents of the reporting. In competitive electoral environments such as most US Senate races, this can lead to a strategic environment resembling a matching pennies game. Based on this observation, we develop a model of bipartisan races where media outlets report about candidates, and candidates make decisions on the type of constituencies to target with their statements along the campaign trail. We develop a methodology to classify news content as suggestive of the target audience of candidate speech, and show how data on media reports and poll results, together with the behavioral implications of the model, can be used to estimate its parameters. We implement this methodology on US Senatorial races for the period 1980-2012, and find that Democratic candidates have stronger incentives to target their messages towards turning out their core supporters than Republicans. We also find that the cost in swing-voter support from targeting core supporters is larger for Democrats than for Republicans. These effects balance each other, making media outlets willing to cover candidates from both parties at similar rates.

Camilo García-JimenoDepartment of EconomicsUniversity of Pennsylvania3718 Locust WalkPhiladelphia, PA 19104and [email protected]

Pinar YildirimMarketing DepartmentThe Wharton School / Univ. of Penn.Philadelphia PA [email protected]

1 Introduction

Scholars agree that free speech, and a free media as its main conduit, are necessary for a

well-functioning liberal democracy. One key role attributed to the media is that of serving

as a watchdog monitoring leaders’ behavior while in office. The media also plays a role in

shaping the behavior of candidates during campaigns. It is especially involved in reporting

about politics during elections, and invests heavily in covering them. Candidates are par-

ticularly aware of the way and extent to which the media reports on them. Most modern

campaigns invest heavily in media relations, and hire specialized staff focused on dealing

and communicating with reporters. It is not uncommon for politicians to be escorted into

campaign locations with political consultants who curate speeches by choosing or omitting

words, phrases, and issues.

Electoral campaigns are not just a game between candidates, but a highly strategic one

between candidates and the media. Candidates use the media to communicate with their

constituencies, and the media uses candidates as sources of news (Bartels (1996); Prat and

Stromberg (2013)). However, this relationship is not purely symbiotic. Although candidates

and media outlets both share the objective of generating news, their preferences can be mis-

aligned regarding the contents of such reporting. First, there are political scandals, which

the media is particularly eager to report about (Fonseca et al. (2014)). The breaking of such

events depends on the previous history of the candidates, and on the increased spotlight at

which the campaign itself puts them. Second, and of more relevance for this paper, through-

out their campaigns candidates need to target a heterogeneous electorate. Particularly in

competitive and bipartisan races, candidates require support from centrist or non-ideological

voters as much as from more ideological or core supporters. The literature often calls the

former swing voters because they are likely to switch their vote across candidates. Core

supporters, in contrast, are unlikely to switch party allegiances, making turnout the relevant

margin of their decision (Cox and McCubbins (1986), Lindbeck and Weibull (1987)).

As a result, candidates have incentives to differentiate their message, especially if it can

be targeted towards core or swing voters. The media, in turn, produces public information

which constrains the targeting ability of candidates. If messages targeted to core supporters

happen to be widely reported by the media, the cost in electoral support among swing voters

may be larger than any benefits that may be reaped from additional core supporters.1 On

the other hand, following and reporting on candidates is costly for media outlets. When

the media devotes more attention to a candidate it may reduce the candidate’s incentive to

1A recent example of this was Mitt Romney’s “the other 47%” statement during a private fundraiser inBoca Raton during the 2012 U.S. presidential election. Although intended for a very narrow audience ofwealthy individuals, its public revelation led to a significant backlash and widespread media coverage.

1

target core supporters, making the gains from such a strategy relatively low. In this paper we

highlight this trade off and explore empirically how it can shape the campaigning behavior

of candidates and the reporting strategies of media outlets, in the context of U.S. Senate

races.

We begin by arguing that these considerations make bipartisan campaigns closely resem-

ble the strategic environment of a classic matching pennies game between each candidate

and the media. Regardless of whether they desire to inform the public or simply earn rev-

enue, as long as there is sufficient heterogeneity in media slant across outlets, the average

media outlet is likely to profit more by reporting or covering statements directed towards

core supporters. These are especially informative for swing voters, and also of interest to core

supporters. In contrast, campaign messages targeted towards swing voters are likely more

‘centrist’ and as such, of little interest to core supporters and of low informational value

to swing voters. Candidates, on the other hand, may benefit electorally from campaign

speech targeted towards core supporters as long as it is not widely reported by the press.

The implication of these conflicting objectives is that candidates’ incentives to target core

constituencies will be determined by how profitable it is for the media to report on them.

Likewise, the media’s incentives to invest in covering campaigns will be determined by the

candidates’ relative profitability from targeting core supporters relative to swing voters with

their campaign speech. In such a strategic environment, both candidates and media outlets

will have strong incentives to behave in a relatively unpredictable way (to the opponent).

In this paper we develop a simple model of bipartisan electoral races with media coverage

and unidimensional policy which we then test empirically. Policy positioning by candidates

happens through their campaign statements, but differences in the core supporter and swing-

voter responses to campaign-trail statements put a limit to full policy convergence. Voters

perceive a candidate as more or less centrist as a function of the history of statements they

have had access to, either through the media or through direct contact with the candidate.

Voters express their preferences throughout the campaign by responding to polls, and lastly,

by voting on election day. Media outlets decide on the intensity with which they will cover

each candidate, and candidates decide the type of statements to make at every date during

the campaign. Modeling electoral races in this way suggests a new meaning for the role of

the media in constraining politicians’ behavior, different from the one emphasized in the

standard political agency framework (e.g., Ferraz and Finan (2011); Snyder and Stromberg

(2010)). Moreover, it suggests a novel channel through which politicians can influence the

media’s behavior that is unrelated to the corruption or influence-buying channels emphasized

in the literature.

We implement this methodology on U.S. Senatorial races for the period 1980-2012. U.S.

2

Senate races offer an ideal empirical setting; most Senate races are high profile, and thus,

enjoy ample media and polling coverage. We show how data on media reports, electoral and

poll results, and an exogenous source of variation in the profitability of campaign reporting

by the media, together with the behavioral implications of the model, can be used to estimate

its structural parameters. We estimate a discrete game of complete information (see Bajari

et al. (2010)) with several novelties. First, the nature of the environment allows us to study

a repeated (and subsequently dynamic) game in a very parsimonious way. This is because

matching pennies games have a unique Nash equilibrium in mixed strategies, and naturally,

electoral campaigns are finite in time as they end on election day. Thus, an unraveling

argument implies that the repeated (and dynamic) game will also have a unique sub-game

perfect equilibrium, hugely simplifying estimation. Second, our empirical strategy allows us

to overcome a pervasive problem faced by the literature on identification in discrete games

of this nature, when frequencies for a subset of game outcomes are unobserved.2

In practice, we estimate a linear model (for the technology mapping equilibrium play

to the electoral outcome of the race) where we allow media outlets to exhibit asymmetric

payoffs from covering Republican and Democratic candidates. We call this media bias, and

show that although it is only partially identified, we can nevertheless recover and compute

its identified set, the equilibrium strategies of all players, and all candidate payoff param-

eters governing the game.3 These directly measure the average impact that different types

of statements and media reports have on the poll standings and electoral performance of

candidates. As will become clear below, we make the linearity assumption only to make our

identification arguments transparent. Our identification strategy closely relies on mapping

conditional probabilities to observed frequencies, and on the availability of an exogenous

shifter of the media’s payoffs. Following ideas in Eisensee and Stromberg (2007) among

others, we collected detailed and high frequency data on sports events from the four most

important sports leagues in the US (the NCAA, NBA, MLB, and NFL). We use these data

as sources of exogenous variation in the media’s willingness to cover and report on politics

during campaigns.

2For example, in entry games, data on the number of firms which decide not to enter in a given period isnecessarily unobserved. Similarly, in our model the media chooses whether or not to cover a given candidate.In periods when the media does not report, we do not observe the type of statement made by the candidate.As a result, we observe the frequencies for different types of statements only conditional on the mediareporting. Nevertheless, we overcome this difficulty tracking changes in candidate support based on polldata over the campaign, which we argue are responsive to the full distribution of statements made, and thus,allow us to to recover all relevant payoff parameters.

3The literature has emphasized how media bias or slant affect the media market (e.g.,Baron (2006);Mullainathan and Shleifer (2005)). In these papers media bias refers to an outlet’s preference for ‘spinning’the information they receive when reporting it. Here our definition of media bias refers only to the media’srelative preference for the extent of reporting about either political party.

3

Our model and estimation require that we measure a signal of the intended target of

each instance of a candidate’s campaign trail speech as reported by the media. As such, our

paper also contributes to the literature by developing and implementing a novel text-analysis

methodology in the spirit of Gentzkow and Shapiro (2010). Our proposed methodology allows

us to assess whether the contents of a given news piece mentions candidate speech suggestive

of swing voter or core supporter targeting. The key idea is to create a self-referential measure.

We first compute the most commonly used phrases related to policy issues found within the

universe of written media coverage of each Senate race (state-x-year). We also compute the

relative counts of candidate name mentions in each article to measure the extent to which

it reports coverage of the Democratic or the Republican candidate. We then assign a score

to each article based on the frequency with which it contains phrases that are relatively

commonly used in articles that mention more heavily one or the other candidate. We can

then use this index to classify each news piece as likely reporting on a core-supporter or a

swing-voter targeted candidate statement. We use different classification criteria to explore

the robustness of our results.

Any attempt to estimate the electoral or poll responsiveness of different types of voters

to candidates’ campaign promises faces a severe identification challenge: unobservables may

drive both the types of statements candidates make and their electoral performance. This

empirical challenge is even more serious when the researcher’s ability to measure candidates’

campaign statements depends on the endogenous decisions of media outlets on whether to re-

port on those statements or not. Our methodology allows us to overcome these identification

challenges.

We use our parameter estimates and empirical findings to assess the impact of partisan

bias in the media, the importance of race characteristics such as the ideological distribution

of voters, and technological innovations altering the cost of media reporting. Our findings

point to a large asymmetry in the strategic environment faced by Democratic and Republican

Senate candidates: on average, the turnout responsiveness of Democratic core supporters is

much larger than that of Republican core supporters, possibly because of the lower turnout

rates of traditionally Democratic demographics.4 This gives strong incentives for the media

to cover Democratic candidates more intensely. Moreover, we also find that swing-voters

punish Democratic candidates more strongly for widely reported core supporter-targeted

campaign speech. As a result, Democratic candidates’ speech is sufficiently disciplined that

in equilibrium Democratic and Republican candidates face similar rates of media coverage

4This finding is consistent with previous empirical studies showing the effect of the media on votingbehavior takes places especially through increased turnout (see George and Waldfogel (2006); Oberholzer-Gee and Waldfogel (2009); Stromberg (2004a)).

4

and reporting. We also find little evidence of significant media preference for reporting on

candidates of one party over the other.

Although we are unaware of any other study modeling the relationship between politicians

and the media in the way we do here, nor estimating the effect of media campaign coverage

on electoral outcomes within a structural model, our paper relates to several research areas.

Foremost, this paper is related to the literature on media coverage (Gentzkow and Shapiro

(2006); Puglisi and Snyder (2008); Stromberg (2004a)). Most of this literature separately

endogenizes policy choices by politicians or coverage decisions by the media. In contrast,

we directly explore the simultaneous determination candidates’ choices and media coverage

strategies. The theoretical literature on issue selection has emphasized how informational

frictions between voters and candidates may affect equilibrium campaign message choices

(Egorov (2015)). The empirical literature also has measured the impact of media coverage

on policy outcomes (Snyder and Stromberg (2010); Stromberg (2004b)). Instead, we focus

on the impact of media coverage on candidate behavior. Thus, our model is close in spirit

to the ideas in Ansolabehere et al. (1992), according to whom “... some of the most crucial

interactions in campaigns are those between candidates and reporters... campaign organi-

zations seek to spoon-feed the press in order to control the news coverage their candidates

receive. Journalists react by striving to keep candidates off balance through independent

reporting” (pg. 72). Another related paper is Fonseca et al. (2014), who study the partisan

bias in newspaper coverage of political scandals in the late 19th Century U.S. They find

significant bias in reporting depending on newspaper partisanship. While they focus on po-

litical scandals only, here we focus on the media’s coverage choices over any candidate-related

content.

Our paper also relates to the literature on transparency, which asks how increased in-

formation affects policy outcomes (Maskin and Tirole (2004); Prat (2005)). Most insights

in this literature follow closely those from the contract-theory literature on agency. In our

model, an increase in the amount of information generated in equilibrium comes from more

intense media reporting, which happens when candidates’ payoffs from speech targeted to

core supporters are higher. Thus, more information may be correlated with more extreme

platform choices by politicians. Of course, if there is no relationship between what can-

didates say during campaigns and what they do while in office, understanding the forces

shaping campaign speech would be uninformative about the media’s role in shaping policy.

Nevertheless, voters appear to care significantly about what candidates say, and the litera-

ture does suggest there is a close relationship between campaign speech and policy choices

(Budge and Hofferbert (1990); Kurkones (1984)).

Also within the tradition of political agency, Besley and Prat (2006) develop a model

5

where the media plays the key role of supplying voters information on incumbent behavior

they use when deciding whether to retain or dismiss him. When the incumbent is able to

influence the media’s information supply decision, it can undermine democracy’s ability to

exert agency control. In this literature, competition in the media market limits the extent

of media capture, and thus, of selection of the information supplied to the public (See for

example Chiang and Knight (2011); Corneo (2006)). In contrast, we show that highly selected

media content can arise even in highly competitive media markets. Our paper also directly

fits within the literature studying how the media affects citizens’ opinions and electoral

choices (e.g.,Campante and Hojman (2010); DellaVigna and Kaplan (2007); Enikolopov et al.

(2011)), and is related to the strand of the literature measuring the media’s ideological

positions (Gentzkow and Shapiro (2010); Puglisi (2006)). Instead of attempting to measure

the ideological positions of different media outlets, we measure the extent of reporting on

speech targeted to different voters by the media as a whole. Although our paper does not

directly study voter learning and the extent to which voters react to new information during

campaigns, our ability to establish an empirical link between overall news reports and poll

changes indirectly suggests voter responsiveness to information, similar to the findings in

Hirano et al. (2015) who study voter learning during primaries and find strong effects for

statewide offices.

Here we model the interaction between politicians and the media as a matching pennies

game. Thus, our paper also is related to the literature that has empirically studied this

kind of strategic environment and the mixed-strategy equilibria it is associated with. Walker

and Wooders (2001) were the first to look for empirical evidence of mixed-strategy behavior

by studying serving on Wimbledon tennis matches. In a very different context, Knowles

et al. (2001) developed a test for racial profiling in motor vehicle searches. In their model,

policemen randomize over searching and not searching potential suspects. Palacios-Huerta

(2003) and Chiappori et al. (2002) similarly studied penalty kick data in soccer to look for

evidence of mixing behavior. To the best of our knowledge, our paper is the first to use this

game-theoretic framework for empirical analysis in a political economy context.

Lastly, our paper contributes to the literature estimating discrete games of complete

information. Most of these have been Industrial Organization applications focused on the

problem of entry, and on pure strategy equilibria (see Berry (1992); Bresnahan and Reiss

(1990, 1991)). In contrast, we estimate a model where only mixed strategies are economically

meaningful, and propose a different identification strategy. Moreover, for games where a

subset of outcomes is unobserved (such as the tax auditing game), Bresnahan and Reiss

(1990) pointed out a negative identification result for the game’s payoff parameters. Our

methodology shows how this issue can be overcome empirically.

6

The rest of the paper proceeds as follows. Section 2 provides a brief overview of electoral

campaigns in the U.S., focusing on Senate races. Section 3 presents our benchmark model

of the campaign trail, Section 4 describes the data, and Section 5 discusses identification

and our empirical strategy. Section 6 goes on to present our main results, and Section 7

concludes. Appendices A and B contain proofs and a detailed description of data sources.

2 Background

In this section we briefly discuss U.S. Senate races and provide some institutional background

on them. The U.S. Senate has been democratically elected for a century now, after the

17th Amendment to the Constitution was passed in 1913. Before the amendment, State

Legislatures elected U.S. senators. The Senate is composed of 2 senators per state; hence

100 senate seats currently exist. Senate elections are held every two years in November of

even years, and senators are elected by plurality within each state. Under the current system,

a third of the seats are up for election on each 2-year cycle, and each seat has a six-year

term. As a result, there are about 33 elections every electoral cycle5.

As in most other elections for public office in the U.S., general elections are preceded

by a period of campaigning, which in practice begins well before each party in each state

has chosen its candidate in either a primary election or a convention. Most states hold

primaries, which vary in how close to the general election they happen. Even during the

primaries pollsters track hypothetical electoral outcomes for the general election. This is

facilitated by the large fraction of Senate races including an incumbent senator, who is very

likely to become his party’s candidate in the general election, and often runs unopposed in

the primary.

Technological change in the media industry has transformed in major ways how electoral

politics operates in the U.S. As access to newspapers first, later television, and more recently,

the internet, have arisen and deepened, not only the quantity but also the kind of information

received by voters has changed. Early on, direct contact between candidates and voters

was reduced. Printed news and television made the media an unavoidable middleman in

the transmission of political messages. Direct contact between politicians and voters, for

example through town-hall meetings and campaign-trail speeches, allowed candidates great

control over the exact contents of their messages. Moreover, during the 19th and early

20th Centuries, the extent of direct control of media outlets by politicians’ families also

contributed to their ability to determine which constituencies were reached by different

messages. In contrast, candidates now have little direct control over how the media will

5After the resignation or death of an incumbent senator, special elections can be held at different times.

7

report on their actions and statements, both because of competition in the media market

and the reduced extent of direct media control by politically involved families. Second,

information has become increasingly public. Before the advent of these new information

technologies, candidates had the ability to target their messages narrowly to specific groups.

This ability has been significantly curtailed by the broad reach of modern media technologies.

According to Ansolabehere et al. (1992, p. 71), “The importance of the mass media and

the growth of television in particular have forced candidates to respond to the routines and

incentives of news organizations. Candidates and their staffs devote a great deal of energy

to influencing the decisions of reporters and editors. Successful candidates and campaigns

also adjust their behavior to exploit the media environment in which they operate.”

These changes manifest themselves in the key role that public and media relations play

within the organizational structure of political campaigns. This is especially so in U.S.

Senate races, which by their nature are quite salient and, as a result, are intensely covered

by both state and national-level media outlets. Interestingly, the very recent emergence of

social media may be allowing candidates to have more direct access to their constituencies

once again. It may also partially allow increased message differentiation and targeting. In

practice, technological change has altered both the costs of campaign coverage by the media,

and the costs and benefits for candidates of producing differentiated messages.

This discussion also motivates our focus on U.S. Senate races. While the number of U.S.

House races is significantly larger, House electoral districts are small relative to most media

markets. This limits the extent to which the media will be directly following individual races.

Furthermore, polling data for House races is scarce. In contrast, U.S. presidential races have

extensive media and poll coverage, but there are too few of them for a satisfactory statistical

analysis. Senate races are, thus, an ideal compromise. Moreover, their state-level nature

implies that the electorate is diverse enough for candidates to have incentives to target

different types of voters.

3 A Simple Model of the Campaign Trail

In this section we describe the simple model of campaign speech and media coverage that we

subsequently estimate. The model captures what we consider are key features of the inter-

action between two candidates running against each other, p ∈ {D,R}, and the distribution

of media outlets m covering the race. In the model, candidates make statements over time

that can be targeted to core or swing voter constituencies. The media decides on coverage

of the campaigns every period, and obtain different payoffs from reporting on either type

of campaign speech. The key assumption we maintain and implicitly test is that payoffs to

8

the media are higher when reporting news on campaign speech targeted to core supporters.

Candidates benefit electorally (in their poll standing) from media reports on their swing

voter-targeted statements. Moreover, although they may also benefit from unreported core

voter-targeted statements, they suffer from media reports of these kinds of statements as

this leads swing-voters to shift towards their opponent.

Time is discrete, t = 0, ..., T , where t = T is election day and t = 0 is the beginning of

the campaign. Both candidates begin their campaigning on the same date. We also assume

that each candidate makes a campaign statement every period. Each media outlet decides

on whether to follow the Democratic candidate D, the Republican candidate R, or both.

Conditional on following a candidate, the media successfully reports on their statements

with an exogenous probability that may vary across parties. Candidate statements and

media reports then map period by period onto changes in poll standings. Our focus on this

paper is not on voters, so we model their behavior in a simple way; voters poll support

decisions at any point in time respond to the amount of information they receive during the

campaign, either directly from the candidates or through the media.

Players’ Actions

Candidates make a statement every period to increase their electoral support. The un-

derlying environment is such that candidates do not fully converge to the median voter’s

ideological stance. This can be easily micro-founded in a model where the turnout of voters

in the extremes of the ideological distribution (core supporters) is sensitive to their distance

to the candidates’ position, and the density of voters is high in the extremes. Standard in-

centives to move towards the median would have to be traded-off against the loss in turnout

from the margins of the distribution of voters. To capture the electoral support of core

voters, candidates are tempted to make ideological statements c, directly targeted to this

audience. Nevertheless, core-targeted statements may decrease the electoral support they

receive from swing voters. Candidates may, instead, make relatively centrist, swing voter-

targeted statements s, which generate little excitement in the extremes, but increases or

maintains the electoral support in the center.

Candidates and the media have partially aligned preferences: candidates benefit from

being reported by the media, and the media profits from reporting news about candidates.

Nevertheless, their preferences are also partly misaligned: candidates benefit from the media

reporting on their relatively centrist statements -those targeted to swing voters-, and are

possibly hurt when the media reports on their ideological statements –those targeted at core

voters. In contrast, the media profits more from reporting on core-targeted statements than

from reporting on swing voter-targeted ones. Candidates also take each others’ strategies

9

as given when deciding their campaign-trail speech. This gives rise to a matching-pennies

strategic environment between each candidate and the media. The reason is simple: the

candidate’s best response is to generate a swing voter-targeted statement when covered

by the media, and to generate core-targeted speech when not covered by it. Similarly, the

media’s best response is to report core-targeted statements and to ignore statements targeted

at swing voters.

Following these ideas, we model the candidates’ action space as follows: each can take

one of two actions every period; either to make a swing voter-targeted statement, or a

riskier core voter-targeted statement: ap ∈ {s, c}. Simultaneously, the media can take one

of three possible actions: to follow both candidates, to follow only D, or to follow only R:

am ∈ {(FDFR), (FDNR), (NDFR)}. In either case, after having taken its action, the media

outlet successfully reports (denoted by χ = 1) with probability P(χ = 1|p) = ηp. This

modeling choice allows us to keep the action space of the media three dimensional, while

still allowing for realizations of periods in which no news reports are observed. Moreover, it

allows us to introduce a parameter, (ηD, ηR), directly capturing the media’s overall propensity

to report differentially about candidates from one or the other party. When ηD 6= ηR, we

refer to this differential treatment as media bias.

Payoffs

The payoff structure is very simple. Every period, the media, m, must pay a cost k per

candidate followed. The per-period gains from reporting on candidate p are:

πp(ap) =

0 if ap = s

πp if ap = c(1)

where we have chosen to normalize the gain from reporting a swing voter-targeted statement

to zero. Nevertheless, we allow the gain for the media to differ between a report about the

Democrat or the Republican.

To simplify the payoff structure of the game, we make some behavioral assumptions about

potential voters. The arrival of media reports can have two effects on voters’ decisions. First,

it can make them shift support from one candidate to the other. Second, it can alter their

turnout decision. This distinction is important because the first margin leads to a zero-

sum setting from the point of view of the candidates, while the second margin does not.

The payoff structure we present below implicitly assumes that core voters only react on the

turnout margin, and never switch party allegiances. In contrast, centrist swing voters only

react on the party support margin, and do not react on the turnout margin (their turnout

10

rate is constant). Voters report truthfully to pollsters.

For candidates, instantaneous payoffs depend on whether their statements are reported

or not, and whether these are targeted to swing voters or to core supporters. Candidates

care about their poll standing, and players’ actions directly map into changes in electoral

and poll support. We suppose that unreported swing voter-targeted statements have no

effect on either core or swing voters. When reported, these kinds of statements do have an

effect on swing voters; they shift support from the candidate not reported to the candidate

reported. Because the turnout rate for swing voters is unaffected, the gain for one candidate

is exactly the loss for his opponent. We also suppose core voter-targeted statements increase

the turnout of core constituencies. When they are unreported, these statements do not have

an effect on swing voters. When they are reported, in contrast, they swing centrist voters

away from the candidate making these statements and towards his opponent. For the stage

game to have a matching pennies structure, this loss must be larger than the gain on the

turnout margin. In such a case, the net effect on the polls from a reported core-targeted

statement is negative for the candidate making it.

We denote by ∆Tap the average change in electoral support to candidate p on the turnout

margin when he chooses action ap, and by ∆Sap the average change in electoral support on

the swing voter margin when candidate p chooses action ap. We can express the change in

poll support for each candidate p ∈ {D,R} between periods t and t+ 1 as:

Vp(t+ 1)− Vp(t) = ∆Tcp1{ap(t) = c, χ(t) = 0}+

(∆Tcp −∆S

cp

)1{ap(t) = c, χ(t) = 1}

+∆Sc∼p1{a∼p(t) = c, χ(t) = 1}+∆S

sp1{ap(t) = s, χ(t) = 1}−∆Ss∼p1{a∼p(t) = c, χ(t) = 1}+εp

(2)

Above, (εD, εR) are other unobserved shocks to the change in electoral support of Democrats

and Republicans. We impose the following parameter restrictions:

Assumption 1. The following inequalities hold:

∆TcD < ηD

(∆ScD + ∆S

sD

), ∆T

cD > 0, ∆ScD > 0, ∆S

sD > 0

∆TcR < ηR

(∆ScR + ∆S

sR

), ∆T

cR > 0, ∆ScR > 0, ∆S

sR > 0

These inequalities are sufficient for the stage game to have a unique Nash equilibrium in

mixed strategies. Equations (1) and (2) and the parameter restrictions in Assumption 1 are

fairly natural. They take into account the zero-sum nature of swing support, and also make

explicit the assumptions that (i) unreported actions by a candidate do not have an effect on

his opponent’s support, and (ii) unreported s statements by a candidate do not have any

effect on his own support. They also imply that candidates gain support from c statements

11

that go unreported, but expect to lose support when these are reported. Finally, they imply

that reported own swing voter-targeted statements increase own support (at the expense

of the opponent), and reported opponent’s swing-targeted statements decrease own support

(and are a gain to the opponent). We further assume that candidates maximize their poll

standing (which, in a bipartisan race, is equivalent to maximizing the winning probability

at every t). In summary, we have a total of eleven structural parameters in this model:

θ = (∆TcD,∆

ScD,∆

SsD,∆

TcR,∆

ScR,∆

SsR, ηD, ηR, πD, πR, k) characterizing the game. Given the

uniqueness of equilibrium we establish below, these also pin down the joint distribution of

players’ actions and poll changes over time.

Indeed, the payoff structure of the game outlined above gives rise to a matching pennies

stage game G. Its normal form representation is presented in Appendix A.

Proposition 1. (Equilibrium Strategies) Suppose ηpπp > k. The normal form game de-

scribed above does not have a pure-strategy equilibrium. The unique mixed strategy equilib-

rium is given by:

γ∗R = 1− ∆TcD

ηD [∆ScD + ∆S

sD](3)

γ∗D = 1− ∆TcR

ηR [∆ScR + ∆S

sR](4)

q∗D =k

ηDπD(5)

q∗R =k

ηRπR(6)

where γD denotes the probability that m plays FDNR, γR denotes the probability that m plays

NDFR, qD denotes the probability that D plays c, and qR denotes the probability that R plays

c. Furthermore, because the stage-game has a unique Nash equilibrium, the only sub-game

perfect equilibrium of the finitely repeated game GT is to play the unique stage-game Nash

equilibrium every period.

Proof. See Appendix A.

As is standard in a matching pennies environment, mixing probabilities are pinned down

by indifference. This makes them a function only of the opponents’ payoffs. In our applica-

tion, this consequence of equilibrium has a subtle testable implication. If we want to study

candidate campaign speech, we must do comparative statics on the media’s payoffs. Candi-

dates’ payoffs are in fact irrelevant to explain their equilibrium behavior. Media payoffs from

reporting on core-targeted statements will be negatively correlated with the equilibrium rate

at which candidates make such statements. This is the sense in which, in our setting, the

12

media can constrain candidates’ behavior. Moreover, the poll gains from a given campaign

statement should have no predictive power for the rate at which the candidate makes such

statements. Conversely, the frequency with which the media reports on the candidates should

be independent of how profitable it is to report. It should depend only on the candidates’

payoffs. Notice also that the ratio q∗D/q∗R = ηRπR/ηDπD does not depend on k.

4 Data

This section describes our data, the construction of our main variables, and the data struc-

ture. First, we discuss the information on all Senate races included in our dataset, the poll

and election outcomes data, and how we rely on poll availability to construct the time di-

mension of our panel. We then introduce our news coverage data and describe the proposed

methodology to compute news article scores measuring the type of content reported. We

conclude by discussing the sports events data we will rely on for our identification strategy.

4.1 Senate Races

For our empirical implementation, we built a dataset of all ordinary competitive races to the

U.S. Senate taking place between 1980 and 2012 for which a Democrat and a Republican

ran.6 Our final sample includes 415 races (out of the 561 = 17 election cycles×33 races that

could have taken place in this 32 year period). For each Senate race we have data on its

outcome (Democratic share and Republican share) from the Federal Elections Commission,

the date and outcomes of the primaries for each party whenever a primary took place –or

whether the candidate was chosen at a party convention for states electing their candidates

that way–, information on whether the incumbent senator was running, and characteristics

of the political environment such as the party of the President, the party of the incumbent

senators in the state, and the share of Democratic and Republican registered voters in the

state. For states without party registration, we use the vote share for President in the most

recent election. Table 1 presents summary statistics for the variables in our study.

4.2 Polls

Our empirical strategy relies on information on the evolution of partisan support throughout

the campaign. We collected detailed polling data for Senate races from a variety of sources.

6We excluded races with three prominent candidates, races where a candidate ran unopposed (or inpractice unopposed), non bipartisan races, and races where either candidate died or quit during the campaign.Appendix B contains a list of dropped races.

13

Descriptive Statistics

Panel A 2-Week Intervals 3-Week Intervals

Dem. All Rep. Dem. All Rep.

Number of poll-to-poll intervals per race 5.63 4.86(4.55) (3.62)

Length of poll-to-poll interval (days) 30.51 35.16(34.32) (35.47)

Number of polls per interval 1.74 2.01(1.66) (2.12)

Electoral support (poll results) 0.44 0.42 0.44 0.42(0.11) (0.11) (0.12) (0.11)

Number of articles per interval 56.11 90.22 41.50 61.98 98.83 45.43(101.7) (127.42) (62.49) (112.53) (138.0) (67.63)

Number of core-targeted articles 35.82 58.79 22.97 41.75 68.43 26.67per interval (0.25 cutoff) (91.09) (102.6) (45.92) (101.52) (113.89) (52.28)

Number of swing-targeted articles 20.29 38.82 18.53 20.23 38.98 18.76per interval (0.25 cutoff) (30.21) (57.67) (30.52) (30.75) (59.30) (31.17)





Number of NFL games per interval 4.22 4.91(fan weighted) (6.34) (6.98)

Number of MLB games per interval 14.91 17.17(fan weighted) (25.43) (27.12)

Number of NBA games per interval 8.91 10.15(fan weighted) (27.65) (28.62)

Number of NCAA games per interval 0.04 0.05(playoffs) (0.29) (0.31)

14

Descriptive Statistics (cont.)

Panel B Dem. All Rep.

Number of races 415

Number of races per election cycle 24.41(7.91)

Number of polls 4076

Number of polls per election cycle 239.76(208.15)

Number of polls per race 10.01(11.93)

Number of news articles 131131 210848 96984

Number of news articles per race 315.97 508.07 233.70(488.13) (687.04) (358.47)

Article score -0.52 -0.005 0.52(0.44) (0.70) (0.43)

Number of media outlets per race 124.17(85.40)

Observations 2337 2033

Table 1: Descriptive Statistics: The table reports means and standard deviations for our main variables.Panel a reports summary statistics for the 2-week poll-to-poll interval panel and the 3-week poll-to-pollinterval panel. Panel b reports overall summary statistics. Please see the text and the data descriptionAppendix B for variable definitions and sources.

To the best of our knowledge, the earliest systematic compilation of polls goes back to

1998. We obtained polls from PollingReport.com for 1998-2004, and from Pollster.com for

2006-2012. For pre-1998 poll data, we did an exhaustive newspaper search using the Dow

Jones/Factiva news database, focusing on all polling reported within a one-year window

before election day.7 We collected a total of 4076 polls. As Table 1 illustrates, we obtain

an average of 240 polls per election cycle, and of 10 polls per Senate race. Naturally, the

frequency of Senate race polls becomes higher in more recent years and in states with larger

populations.

7For example, for the 1998 election we began our search on November 1, 1997. In a few cases weencountered discrepancies in the reported polling results across articles from different newspaper sourcesreferring to the same poll, in which case we averaged the results. The 1998 poll data from PollingReport.comwas sparse, so we also did an online newspaper search for polls for that year. When only the month of thepoll was reported we imputed the date to be the fifteenth of the month except for November polls, in whichcase we imputed the date to be the first of the month.

15

P0 P1 P2 P3 P4 (T )

Actual Polls −→

k-week Poll Averages −→

Poll 1 Poll 2 Poll 3 Poll 4 Poll 5 Poll 6 Poll 7 Poll 8 Election Day

k weeks k weeks k weeks k weeks

Figure 1: Construction of the poll-to-poll intervals.

Our empirical strategy also relies on our ability to compute frequencies of news reporting

over time. To do this, we rely on our dataset of polls to construct what we call “poll-to-poll”

intervals. By using the poll dates to create poll-to-poll time intervals within each race, we

effectively create the time dimension of our panel. Subsequently, we use the dates of the

news articles to assign them to their corresponding poll-to-poll interval, within which we

measure the different news article statistics required by our empirical strategy, and which we

describe in section 4.3. Because the definition of these periods is arbitrary, we explore two

alternative criteria for the construction of the intervals, by grouping nearby polls using two-

week or three-week windows, and averaging –weighting by poll sample size– all polls falling

within the time window. We then assign the median date among the polls in the window as

the period marker. This strategy is convenient because the frequency and spacing of polls is

uneven across states and years, and because aggregating nearby polls helps us average out the

inherent measurement error in poll reports. Figure 1 graphically illustrates the construction

of the poll-to-poll intervals.

The construction of time periods in this way introduces an unavoidable precision/bias

trade-off because the statistics we construct are based on observed news article relative

frequencies. On the one hand, the longer a poll-to-poll interval, the smaller the sampling

error in the measured statistics of news reports falling within it, and the closer these statistics

will be to the probabilities with which they are generated. On the other hand, if the actual

probabilities change significantly over time, –for example because payoff parameters depend

on a time-varying state variable–, the longer a poll-to-poll period, the larger the bias from a

statistic based on frequency counts within the interval. To deal with this issue, we explore the

robustness of our results to alternative definitions of a poll-to-poll interval, and we perform a

robustness exercise where we estimate a version of the model where the game is not repeated

but dynamic. In that case, we allow the payoff parameters to evolve as a function of a state

variable, namely the current relative poll standing of the candidates.

16

4.3 Measuring News Reporting

Estimation of our model requires us to classify different types of observed news article content

related to the political campaigns. This allows us to establish a link between reported

candidate speech and electoral performance. More specifically, we require a classification

criterion of each news piece as suggestive of turnout (core supporter)-targeted or swing

voter-targeted campaign speech. Naturally, such a distinction is empirically meaningful only

in relation to the ideological distribution of the relevant population of potential voters –the

state in our setting. For example, the same statement may be considered moderate and

targeted to centrist voters when expressed by a Democratic candidate in Massachusetts, but

it may only appeal to core Democratic voters when expressed by a Democratic candidate in

Utah. Moreover, the ideological distribution of the population within a state may change

over time, making a statement that could be considered core-targeted in 1980, appealing to

swing voters in 2012. A sensible classification criterion for the reported content of media

reports must be race-specific.

With this in mind, we follow some of the ideas in the seminal work of Gentzkow and

Shapiro (2010) for computing measures of media slant, to develop a novel index of media

content. For each race, we conducted a comprehensive search of news reporting from two

major news databases, Lexis Nexis and Factiva, which cover national and local newspapers.

The search criteria was based on the names of both candidates in each race, during the

year prior to election day.8 We collected all news articles mentioning either candidate in a

given race. Our initial search recovered more than 300,000 articles covering 560 races and

1120 candidates. For the set of articles mentioning either candidate in a given race, we

implemented a text search algorithm to parse the HTML tags and gather information about

the articles (publication date, source, subjects, and persons mentioned in the article). These

tags allowed us to further weed out irrelevant articles and omit repeated articles. As Table

1 illustrates, our estimation sample contains information from 210,848 news articles, with

an average of 508 articles per race. Although articles often mention both candidates, the

average article is usually centered on reporting about one of them. The name of the opponent

is reported as part of the context only. A few articles, of course, discuss the race as a whole

and would be harder to classify as reporting about the Democrat or the Republican. We

rely on the candidate name information in the articles themselves for the construction of our

index of news reporting.

We proceed in the following way. First, to assess the extent to which an article reports

on the Democratic or the Republican candidate, we count the number of times the name of

8We downloaded these articles in HTML (for Lexis Nexis) and .rtf (for Factiva) formats

17

Figure 2: Distribution of article name assignments τi.

each appears in the article. We then compute the candidate assignment statistic τi:

τi =xRi − xDixRi + xDi

∈ [−1, 1]

where xpi is the count of party p’s candidate name in article i. Values closer to +1 imply

the article is more heavily reporting on the Republican, and values closer to −1 imply the

article is more heavily reporting on the Democrat. Figure 2 presents the distribution of τi

across all articles and races. The distribution is multi-modal, with most articles referring

heavily to just one candidate. There is also some significant density of articles mentioning

both candidates evenly (with scores close to 0). Table 1 reports the number of articles we

classify as referring to the Democratic (τi < 0) and Republican (τi > 0) candidates. The τi

provides us with a continuous measure that allows us to classify the contents of all articles

in each race.

Within the set of all articles corresponding to a given race, we identify the 500 most

commonly used 2 word phrases (2-grams), and the 500 most commonly used 3-word phrases

(3-grams). We then proceed by giving a score sj ∈ [−1, 1] to each phrase j ∈ {1, 2, ..., 1000},related to how Republican-specific vs. Democratic-specific the phrase is within the set of

articles covering the race. We do this by computing a weighted average of the τi’s corre-

sponding to articles containing phrase j, where the weights are the frequencies with which

each phrase appears in each article, relative to all articles covering the race. Formally, for

18

Figure 3: Distribution of articles scores σi.

each j,

sj =

∑i τifij∑i fij

∈ [−1, 1]

Here fij represents the frequency with which phrase j appears in article i. For example, if

a given phrase appears only in articles that only mention the Republican candidate, then

that phrase will have a score of sj = 1. sj gives gives us information regarding the extent

to which phrase j is more commonly associated to one candidate or to the other. Endowed

with the score sj for each phrase in the race, we then compute a score for each news article in

the race, building a weighted average of the scores of phrases appearing in the article, where

the weights are the frequencies with which each phrase appears in each article, relative to

all phrases in the article. Formally for each i,

σi =

∑j sjfij∑j fij

∈ [−1, 1] (7)

Articles with more phrases which, within the race coverage, are more closely associated with

articles more heavily covering the Republican (Democratic) candidate will get higher (lower)

scores. This measure has the advantage of being completely self-referential; we do not use any

information from outside the coverage of the specific race to assess the extent to which a given

news piece is likely to be reporting about core supporter or swing voter-targeted statements

by the candidates. σi is a continuous index which we use together with τi, to classify each

article both as covering either the Democrat or the Republican, and whether the content is

19

-1 -0.25 0 0.25 1

Core-targeted for D Swing-targeted for D

Swing-targeted for R Core-targeted for R

Figure 4: Illustration of the Article Type Classification (0.25 score cutoff case).

more swing voter targeted –s– or core supporter targeted –c– (depending on the value of

σi). Figure 3 presents the distribution of the article scores σi for our sample of news pieces.

Our benchmark specification classifies articles as signaling core supporter-targeted speech

when σi < −0.25 for the Democrat and when σi > 0.25 for the Republican. It classifies the

remaining articles as signaling swing voter-targeted speech (those with scores σi ∈ [−0.25, 1]

for the Democrat and with scores σi ∈ [−1, 0.25] for the Republican). Figure 4 illustrates

graphically the article classification criterion for the ±0.25 cutoff. In our robustness analysis

we present additional results that reclassify all articles using alternative cutoffs σi = ±0.5

and σi = ±0.75.

Our collection of news articles also allowed us to obtain information on the number of

different media outlets covering each race. We obtained this information based on the media

outlet name and date tags in the articles. As a result, we have data on the count of different

outlets reporting on a race within each poll-to-poll interval.9 Finally, to compute overall

reporting frequencies, we defined the total effective number of periods or stage games within

each poll-to-poll interval as the number of days between polls times the total number of

media outlets ever reporting on the particular race. This is equivalent to assuming that the

candidates play a stage game against each media outlet every day during the campaign.

4.3.1 A Cross-validation exercise

Our theoretical model of campaign-trail speech is based on the premise that the media

profits relatively more from reporting on candidate speech targeted to core supporters. To

the extent that this premise is correct, a revealed-preference argument would suggest that

written media outlets should be willing to allocate more space to news pieces covering these

kinds of campaign speech. As a cross-validation exercise of our index of media content σi, in

9In order to remove misclassifications due to the occasional use of “the” in front of an outlet name (e.g.,The New York Times could occasionally be classified as New York Times), we processed the text to removethe word “the” in front of all outlet names.

20

Conditional Correlations of Article Word Counts and Article Scores

Dependent variable: Number of Words Log Number of Words

(1) (2) (3) (4)

Absolute value of article score (|σi|) 36.83 40.10 0.052 0.036(29.98) (17.69) (0.031) (0.016)

Race Fixed Effects N Y N Y

R2 0.02 0.06 0.09 0.29No. of Races 417 417 417 417No. of Observations 176034 176034 176034 176034

Table 2: Article Word Counts: The table presents OLS panel regressions of a measure of article wordcount on the absolute value of the article’s score σi. The dependent variable in columns (1) and (2) is theword count of the article. The dependent variable in columns (3) and (4) is the log of the word count ofthe article. All models control for the article candidate assignment score τi, the article’s days to electionand its square, and include year fixed effects and a constant. Columns (2) and (4) include race fixed effects.Standard errors are robust to arbitrary heteroskedasticity and clustered at the Senate-race level.

Table 2 we look at the relationship between the number of words in an article in our sample,

and the absolute value of its score σi. The table presents results from OLS specifications using

either the number of words or its log, with and without race fixed effects. All specifications

control for the article’s candidate assignment score τi, a quadratic in the article’s date, and

year fixed effects. The conditional correlation between article length and σi is always positive,

and is highly significant in the models including race fixed effects which exploit within-race

variation only. The mean word count of articles in our sample is around 800 words. From

column (2) in Table 2, moving from a score of 0 to a score of 1 increases the article’s length

by 40 words, or around 5% of the average article length. This suggests that our proposed

index is a reliable signal of the article content relevant to our model.

4.4 Sports news data as media-payoff shifters

In our empirical strategy we exploit the observed correlations between frequencies of news

reporting and changes in poll support for both candidates. Changes in electoral support

along the campaign may be due to a host of unobservables (to the econometrician) which

may, in turn, be correlated with candidates’ incentives to make different kinds of statements

and the media’s incentives to cover campaigns. To overcome this difficulty we rely on the

occurrence of major sports events as exogenous shifters of the media’s attention, similar

to Eisensee and Stromberg (2007). More specifically, we collected daily information on all

games from the NFL, MLB, and NBA, and all playoffs games from the NCAA between

21

1979 and 2012.10 This constitutes a dataset with more than 600,000 observations. For each

day we have information on whether a team played or not, and won or lost the game. We

then match teams to their respective states, which gives us daily state-level variation in the

media’s payoff from reporting on political campaigns. This source of variation is unlikely to

be related to unobservables driving candidate behavior along the campaign trail. Because

most games for each sports league take place during a specific season of the year (e.g., football

is concentrated in the winter, and baseball in the summer, for example), having information

from the four leagues provides us with year-round variation.

Some states do not have teams in these leagues, or their teams seldom make it to the

playoffs with enough frequency during the 33 year period. To obtain exogenous variation in

media campaign coverage also for these states, we additionally collected information from

Facebook. Facebook collected county-level information on the distribution of “likes” among

its users in 2013, for each NFL, MLB, NBA, and NCAA team. We use this information

as a proxy for the extent to which the media covering a race in a given state may vary

its behavior in response to salient sports events from teams of other states, which have a

significant support in the state where the race is taking place. We computed the matrices

WNFL, WMLB, and WNBA, where entry wlij, l ∈ {NFL,MLB,NBA} records the total

population of counties in state i, as a fraction of total state population, where a plurality

of Facebook users supports a team from state j in the sports league l. For states without

teams in our data, these matrices provide us with variation in media payoffs, coming from a

large fan base rooting for out-of-state sports teams that may lead to local media attention.

Figure 5 illustrates the geographic distribution of fans of the teams in these four leagues,

illustrating the straddling of fans across states which we exploit.11

10NFL is the National Football League, MLB is the Major League Baseball, NBA is the NationalBasketball Association, and NCAA is the National Collegiate Athletic Association.

11The Facebook fan map for the NCAA reveals that fandom for College Football is very highly correlatedwith state boundaries, thus giving us no additional variation. For this reason, we do not weight NCAAsports events by the cross-state fandom weighs.

22

Fig

ure

5:Facebook

Sp

ort-

Tea

mF

ans

Dis

trib

uti

onM

ap

s.

23

5 Empirical Strategy and Identification

We now discuss our empirical strategy. Our purpose is to recover the payoff parameters

governing the matching pennies game described above. The empirical strategy has several

components. We first discuss the non-parametric identification of the equilibrium mixing

strategies of all players based on the counts of the different types of news articles in our

dataset. We then show how, relying on these mixing strategies, on polling data, and on

the exogenous source of variation in campaign news coverage induced by the sports events,

we can identify the electoral response elasticities that map directly on to the game’s payoff

parameters for the candidates. This is despite our inability to observe a subset of the

equilibrium outcomes of the game, namely realizations in which the media does not report

on the campaign.

5.1 Identification of the mixing strategies

Our first task is to develop a methodology allowing us to identify the model parameters θ

using the equilibrium conditions (3)-(6), and the data on media reports and poll and election

results. The main difficulty in identifying payoff parameters from behavior reflecting mixed

strategies in a setting such as this one is the nature of the game itself; we do not observe

counts of type c or s candidate statements in periods when the media does not report on

the campaign.

We first introduce some notation. Define Xap (t, t+τ) as the count of type a ∈ {c, s} media

reports on candidate p ∈ {D,R} appearing between stage games t and t + τ . Also define

Nap (t, t+ τ) as the count of type a campaign-trail statements by candidate p between stage

games t and t+ τ that do not get reported by the media. While the Xap (t, t+ τ) are observed

(with error), the Nap (t, t+τ) are unobserved. If within a time interval [t, t+τ) payoff param-

eters θ are constant, the repeated matching pennies game directly gives us the joint distribu-

tion for the four observables and the four unobservables (XcD, X

sD, X

cR, X

sR, N

cD, N

sD, N

cR, N

sR).

In fact, for each candidate, (Xcp(t, t + τ), Xs

p(t, t + τ), N cp(t, t + τ), N s

p (t, t + τ)) is a draw

from a multinomial distribution with success and failure probabilities determined by the

equilibrium mixing strategies of candidates and media outlets.

Correspondingly, each observed count Xap has a binomial marginal distribution given by

P(Xap (t, t+ τ) = k) =

(τ

k

)(ϕap)k (

1− ϕap)τ−k

(8)

where ϕcp ≡ q∗p[1 − γ∗∼p]ηp and ϕsp ≡ (1 − q∗p)[1 − γ∗∼p]ηp. The expressions in equation (8)

24

result from equilibrium play: q∗p is the probability that candidate p chooses a core-targeted

statement each period, and [1−γ∗∼p]ηp is the unconditional probability that the media reports

on candidate p each period.12 Because the Xap are observable, equation (8) allows us to non-

parametrically identify the conditional probabilities generating the observed media reports,

by noticing that the MLE estimator for a binomial random variable is simply its sample

analogue:

ϕap(t, t+ τ) ≡Xap (t, t+ τ)

τ(9)

The estimator in equation (9) gives us four equations in six unknowns (q∗D, q∗R, γ

∗D, γ

∗R, ηD, ηR).

Nevertheless, by taking the quotients of these conditional probabilities for each p, we can

recover the equilibrium mixing strategies of both candidates:

ϕspϕcp

=(1− q∗p)[1− γ∗∼p]ηpq∗p[1− γ∗∼p]ηp

⇒ q∗p(t, t+ τ) =ϕsp(t, t+ τ)

ϕsp(t, t+ τ) + ϕcp(t, t+ τ)(10)

The efficient estimator of the q∗p(t, t + τ)’s will be the one taking t = 0, τ = T . Moreover,

from the definition of the ϕap’s and equation (9) for p ∈ {D,R}, we can also recover the

conditional probabilities of a news report of any type about candidate p:

φp(t, t+ τ) ≡ [1− γ∗∼p]ηp = ϕcp(t, t+ τ) + ϕsp(t, t+ τ) (11)

Equation (11) also illustrates that in this model, and based on the observed article

counts, we cannot separately identify the average media biases (ηD, ηR) from the equilibrium

mixing strategies (γ∗D, γ∗R) of the media. The reason is that in stage games where a news

report is not observed, we cannot distinguish whether this happened because the media did

not invest in following the candidate, or because despite doing so, a news piece was not

generated. We do not observe the realizations of the unobserved speech (N cD, N

sD, N

cR, N

sR).

However, our ability to recover estimates of equilibrium reporting rates and of the equilibrium

mixing strategies of candidates implies we have estimates of the parameters governing the

12We can additionally calculate the conditional distribution of the unobserved counts Nap using the infor-

mation from the observed ones. This distribution is also binomial and takes the form:

P(N cp(t, t+ τ) = k|Xc

p(t, t+ τ), Xsp(t, t+ τ)) =

(τ −Xc

p(t, t+ τ)−Xsp(t, t+ τ)

k

)×

[q∗p[1− (1− γ∗∼p)ηp]

(1− γ∗∼p)ηp

]k [1−

q∗p[1− (1− γ∗∼p)ηp](1− γ∗∼p)ηp

]τ−Xcp(t,t+τ)−Xs

p(t,t+τ)−k

This conditional distribution can be derived by noticing that 1 − (1 − γ∗∼p)ηp is the total probability thatthe media does not report on candidate p each period. There is an analogous expression for the conditionaldistribution of N c

p(t, t+ τ) which we omit here to save space.

25

conditional distributions they are drawn from. Below we show this will be sufficient to

recover the candidates’ payoff elasticities ∆, arguably the parameters of most economic

interest. Furthermore, as we will show below, exploiting the variation in polls and election

results, we will also be able to provide an identified set for the ηp’s, the γp’s, and relative

media payoffs πR/πD.

5.2 Identification of the electoral performance technology

We now discuss our identification strategy for the elasticities mapping equilibrium outcomes

to changes in polls over time. Although a linear model for the changes in candidate shares

of electoral support is necessarily misspecified, it makes our identification arguments trans-

parent. It also illustrates clearly what the sources of variation we exploit are, to identify the

candidates’ payoff parameters. Recall the construction of our poll-to-poll intervals, and con-

sider the realizations of all game outcomes within stage games t and t+τ .13 The proposition

below establishes how the core-supporter turnout elasticities (∆TcD,∆

TcR) can be recovered.

Proposition 2. (Identification of Turnout Elasticities) Consider the following linear speci-

fication:

VD(t+ τ)− VD(t) + VR(t+ τ)− VR(t)

τ= ∆T

cD

ϕcD(t, t+ τ)

φD(t, t+ τ)+ ∆T

cR

ϕcR(t, t+ τ)

φR(t, t+ τ)+ ω(t, t+ τ)

(12)

where ϕap(t, t+ τ) and φp(t, t+ τ) are defined in equations (9) and (11), and ω(t, t+ τ) is an

error term derived in Appendix A. Suppose instrumental variables z(t, t + τ) are available,

such that, (i) πp(z) vary with z, (ii) Cov(z, ω) = 0, and (iii) the dimension of z is at least 2.

Then a 2SLS regression of equation (12) using z as instruments for ϕcD(t, t+ τ)/φD(t, t+ τ)

and ϕcR(t, t+ τ)/φR(t, t+ τ) identifies the elasticities (∆TcD,∆

TcR).


The dependent variable in equation (12) is the change between two time periods in the

fraction of polled individuals reporting support for neither the Democratic nor the Repub-

lican candidate. In most polls, these are people who have not made up their mind about

whether to turn out or about which candidate they prefer. Proposition 2 shows that the

13In practice, the length of a panel period, τ , will be determined by the frequency of polls for the raceas we described in section 4.2. As long as pollsters’ poll-timing decisions are not dependent on how themedia is covering the campaigns or how the campaign is developing, choosing the panel periods this way willintroduce no additional sources of bias when estimating equation A.5. In section 6.3.2 we test the plausibilityof this assumption.

26

covariation in these changes with the ratios of news reports indicative of core-targeted state-

ments to all news reports for each candidate can identify the average turnout response of

the polled electorate to core voter-targeted statements. The result hinges on aggregating

the changes in poll standings of both candidates; the zero-sum nature of swing voter-voter

support implies that all swing voter effects cancel out after this aggregation.

The proof of this result proceeds by first writing down the net change in the poll standing

of a given candidate between stage games t and t + τ from equation (2), as a function of

the counts of all realizations of game actions that affect the evolution of electoral support

(Xcp, X

c∼p, X

sp , X

s∼pN

cp) in that time interval. After adding the net changes for both candidates

and dividing by the number of stage games considered, all terms related to swing voters

cancel and we obtain an expression that depends only on (N cp(t, t+ τ) +Xc

p(t, t+ τ))/τ for

p ∈ {D,R} and the average of the shocks in the time interval (see equation (A.6) in Appendix

A). A first empirical challenge is that this equation cannot be estimated directly; the counts

of unreported core-targeted statements (N cD(t, t + τ), N c

R(t, t + τ)) are unobserved. This

difficulty can be overcome by noticing that E[(N c

p(t, t+ τ) +Xcp(t, t+ τ))/τ

]= q∗p is simply

the expected fraction of stage games in which candidate p will target his core supporters.

We can then use our non-parametric estimate for the equilibrium mixed strategy of the

candidate from equation (10), and express (N cp(t, t+ τ) +Xc

p(t, t+ τ))/τ as our estimate of

q∗p, namely ϕcp(t, t + τ)/φp(t, t + τ), plus sampling noise that goes to zero at rate√τ as the

poll-to-poll interval size increases.14

The second challenge in estimating equation (12) is the endogeneity of ϕcD(t, t+τ)/φD(t, t+

τ) and ϕcR(t, t + τ)/φR(t, t + τ). Each of these is likely correlated with other unobservables

that also determine the evolution of electoral support during a campaign, so we require

at least two instrumental variables. These need to be sources of variation for the relative

frequencies of core-targeted statements made by candidates, which do not, simultaneously,

covary with any other determinants of the evolution of electoral support during the cam-

paign. Our model suggests what the natural instruments for these variables should be. From

the equilibrium mixing probabilities in equations (5) and (6), the mixing probabilities chosen

by the candidates are pinned down by the media’s payoffs from reporting:

q∗p(z) =k

ηpπp(z)(13)

A shifter of the media’s payoffs to reporting on the campaign, which is otherwise unrelated

to other campaign outcome determinants, will generate variation in the candidates’ choices.

14Expressing the regressors in this way in equation (A.6) amounts in practice to including an explanatoryvariable with classical measurement error, which should create no additional issues as long as our instrumentsare valid.

27

As long as such an instrument varies across poll-to-poll intervals, it can be used to identify

the parameters of interest from equation (12). Equation (13) also points out that the model

makes an unambiguous prediction about the expected sign of the first stage; if larger values

of the instrument reduce the media’s profitability of reporting on politics, this should increase

the rate at which the candidates target their core constituencies. Thus, we should expect a

positive sign for the first stage. As we described in section 4.4, we rely on salient sports events

which may crowd out the media’s attention (thus, lowering its payoff from reporting on the

campaigns). Eisensee and Stromberg (2007) use time variation generated by the occurrence

of the Olympic Games to study media coverage of natural disasters. In a similar spirit, we

use daily data on the occurrence of games in any of the four major sports leagues in the U.S.

(MBL, NFL, NBA, NCAA). We match the games to the poll-to-poll intervals where they

fall, including games with teams from the race’s state or from other states with a significant

local fan base as proxied by the Facebook fandom data (see section 4.4). The exclusion

restriction is thus that games in any of these sports are uncorrelated to any unobserved

determinants of the evolution of electoral support besides how they alter the media’s relative

payoffs from covering the campaigns. We believe this is a plausible exclusion restriction.15

Moreover, because the model predicts the sign of the first stages, we consider the first stages

as implicit specification tests of our model.

Equipped with estimates of ∆TcD and ∆T

cR, we now describe the identification of the

remaining electoral support elasticities.

Proposition 3. (Identification of Swing Elasticities) Consider the following linear specifi-

cation:

D(t, t+ τ)− R(t, t+ τ)

2= ∆S

sDφD(t, t+ τ)τ −∆SsRφR(t, t+ τ)τ + ζ(t, t+ τ) (14)

where

p(t, t+ τ) ≡ [Vp(t+ τ)− Vp(t)]− ∆Tc∼p

ϕc∼p(t, t+ τ)

φ∼p(t, t+ τ)τ

is the change in electoral support for candidate p net of the turnout effects of the opposing

candidate, and ζ(t, t + τ) is an error term derived in Appendix A. Suppose instrumental

variables z(t, t + τ) are available, such that, (i) τ(z) varies with z, (ii) Cov(z, ζ) = 0, and

(iii) the dimension of z is as least 2. Then an IV regression of equation (14) using z as

15One possible channel through which the exclusion restriction may fail is if the occurrence of these sportsevents directly either lowers the turnout or changes the voters’ electoral choices. Healy et al. (2010), forexample, find that college football wins around election day increase the vote share of incumbent Senators.This effect is restricted to matter only around election day, thus only for the last poll-to-poll interval in eachrace. As robustness checks we estimate the model excluding the last period of each race, and using onlyvariation in games won instead of variation in games taking place.

28

instruments for φD(t, t+ τ)τ and φR(t, t+ τ)τ identifies the elasticities (∆SsD,∆

SsR). Finally,

(∆ScD,∆

ScR) are identified from

∆Scp =

∆Tcp

φp− ∆S

sp (15)


Proposition 3 shows that the covariation between appropriately “corrected” changes in

the competitiveness of the race over time and the rate at which candidates are being reported

about any type of statements can identify the average swing voter response of the polled

electorate to swing voter-targeted statements. The correction term, ∆Tc∼p

ϕc∼p(t,t+τ)

φ∼p(t,t+τ)τ captures

poll changes induced by core-targeted statements from the opponent. Although these do not

directly affect the poll standing of the candidate (see equation (2)), in equilibrium they do

so indirectly. As equation (15) shows, the poll gains to a candidate from core supporter-

targeted statements by his opponent, ∆Scp, are fully pinned down by equilibrium play and

the remaining elasticities. The proof of Proposition 3 shows that relying on this equilibrium

relationship we can use the estimates of (∆TcD,∆

TcR) from Proposition 2 to appropriately

correct for poll changes stemming from core-targeted candidate speech.

Subsequently, by scaling the net poll change in the interval by its size (the corresponding

number of stage games), we obtain an expression where the regressors depend on τ but

the error term does not. This is key to our identification strategy. The reason is that in

equation (14) both φp(t, t + τ)τ ’s will be correlated with other unobservables in ζ(t, t + τ)

driving the evolution of the campaign. We require the use of appropriate instruments once

more, and we again rely on exogenous variation induced by sports events. The variation

in this case is of a different nature, however. In contrast to the identification idea for

the elasticities in Proposition 2, where we leveraged the dependence of q∗p on the media’s

payoff from reporting on politics πp, our model implies that the equilibrium reporting rate

E[φp(t, t+ τ)

]= ηp(1 − γ∼p) is independent of πp. As equations (3) and (4) show, in

equilibrium the reporting rate depends only on the candidates’ payoff parameters, which are

unlikely to respond to variation in sports events.

Nevertheless, the right-hand side variables in equation (14) are scaled by the size of the

poll-to-poll interval. If the occurrence of sports events leads to variation across media outlets

in their willingness to report on politics, then sports events can be valid shifters of τ(z), and

thus valid instruments.16 Sports events induce no intensive-margin response by a given media

outlet (whose reporting strategy is pinned down by indifference). They can, nevertheless,

induce an extensive margin response across the distribution of media outlets covering a race.

16Recall that in equation (14), ζ(t, t+ τ) is independent of τ .

29

0

πp

Sports Events

πp(z)

z0 z1

Fraction of reporting media outlets at z0

Fraction of reporting media outlets at z1

Variation Induced by the Instrument

Figure 6: Instrument variation and media coverage in the extensive margin.

Figure 6 illustrates how variation in sports events can lead to infra-marginal outlets (those

barely not covering the race in a given period) to enter coverage, or to supra-marginal outlets

(those barely covering the race in a given period) to drop out from coverage. In the figure we

plot a hypothetical distribution of media outlets who are heterogeneous in their payoffs from

covering the campaign. Across the board, their payoff from campaign coverage is decreasing

in the occurrence of relevant sports events, and only those outlets with a positive payoff

invest in covering the campaign. When more sports events take place in a given period,

some media outlets stop covering the campaign, effectively lowering the number of stage

games τ being played. We exploit this source of variation to instrument for the endogenous

variables in equation (14). As this discussion points out, our model once again makes an

unambiguous prediction about the expected sign of the first stages for equation (14). In this

case, the model predicts a negative relationship between the intensity of sports events and

the two endogenous variables in the structural equation. The model also predicts a positive

estimate for the IV second-stage coefficient on φD(t, t + τ)τ , and a negative estimate for

the coefficient on φR(t, t + τ)τ . These sign predictions are further specification tests of our

model.

In Table 3 we directly test this mechanism in our data, by looking at the correlation

between sports events and the number of distinct media outlets from which we observe news

pieces over time. We find evidence that the number of media outlets covering a senate

30

Testing Model Assuptions: Media Coverage and Sports Events on the Extensive Margin

Dependent variable:No. of reporting media outlets in poll-to-poll interval

Total no. of reporting media outlets in the race

2 week poll-to-poll intervals 3 week poll-to-poll intervals

Regressor (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Log NFL games/τ −0.008 −0.005(0.029) (0.036)

Log MLB games/τ −0.021 −0.042(0.019) (0.021)

Log NBA games/τ −0.035 −0.041(0.018) (0.021)

Log NCAA games/τ −2.335 −2.046(0.609) (0.658)

Log all games/τ −0.062 −0.085(0.017) (0.020)

R2 0.69 0.69 0.69 0.70 0.70 0.70 0.70 0.70 0.70 0.70No. of Races 415 415 415 415 415 415 415 415 415 415No. of Observations 2134 2134 2134 2134 2134 1865 1865 1865 1865 1865

Table 3: Testing Model Assumptions: Media Coverage and Sports Events on the Extensive Margin.The table presents OLS panel regressions. The dependent variable in all columns is the number of mediaoutlets reporting on a race in a poll-to-poll interval as a fraction of all media outlets ever reporting on therace. All models include a full set of Senate-race fixed effects, month fixed effects, a dummy variable for thelast poll-to-poll interval in the race, and a constant. The first five columns of the table are estimated on the2 week poll-to-poll interval panel. The last five columns of the table are estimated on the 3-week poll-to-pollinterval panel. Columns (1) and (6) include the log number of NFL games per day, columns (2) and (7)include the log number of MLB games per day, columns (3) and (8) include the log number of NBA gamesper day columns (4) and (9) include the log number of NCAA games per day, and columns (5) and (10)include the log number of NFL, MLB, NBA, and NCAA games per day. All regressions are weighted bythe square root of the length in days of the poll-to-poll interval (relative to the longest interval). Standarderrors are robust to arbitrary heteroskedasticity.

race does vary systematically with sports events relevant to the race’s state. We test this

assumption relying on our dataset of news articles, which includes the media outlet names

for each news piece. This allows us to compute the number of different outlets producing

news for a given race over time. The table reports OLS results of a regression where the

dependent variable is the number of distinct media outlets reporting on a senate race in

a given poll-to-poll interval as a fraction of all media outlets ever reporting on that race,

on each of our sports events instruments. These models include Senate-race fixed effects,

exploiting only within-race variation. The table presents results both for the 2-week and

3-week poll-to-poll interval datasets we described in section 4. All regressions show evidence

of a significant and negative within-race correlation between game frequencies and media

outlet coverage on the extensive margin.

31

6 Estimation Results

In this section we present our main empirical findings and discuss several robustness exercises.

We first present our point estimates for the poll change elasticities ∆, and conclude with a

partial identification exercise for the media biases (ηD, ηR). Overall, we find that the turnout

margin response to core-targeted speech is more responsive for Democratic candidates and

that the swing voter response to swing-targeted speech is quantitatively similar for Democrats

and Republicans. We also find that the responsiveness of swing voters to swing-targeted

speech is lower in states with a more uneven partisan distribution of voters. Nevertheless,

we do not find evidence suggesting that voter responsiveness to media coverage significantly

changes as the campaigns develop. Our results also indicate that Democratic candidates

suffer larger swing voter losses when their core-targeted campaign speech is widely reported

by the media compared to those of Republican candidates. Finally, we find that a large bias

of the average media outlet towards either party is unlikely.

6.1 Poll Change Elasticities

Our empirical strategy consists of several steps. On our state-x-race-x-poll-to-poll interval

dataset, we compute the average counts of reported core-targeted statements for each can-

didate within a poll-to-poll interval ϕcp,r,t ≡Xc

p,r,t

τr,t, and the average counts of total reported

statements for each candidate within a poll-to-poll interval φp,r,t ≡Xc

p,r,t

τr,t+

Xsp,r,t

τr,t. p ∈ {D,R}

denotes the candidate’s party, r denotes the race, t ∈ {1, 2, ...Tr} denotes the poll-to-poll

interval, Tr is the last poll-to-poll interval of race r, and τr,t denotes the number of stage

games within poll-to-poll interval t for race r (computed as the days in the poll-to-poll

interval times the number of total media outlets ever reporting on the race).

Following Proposition 2, we estimate the turnout effects of core-targeted statements by

2SLS using the following model:

4tvDr +4tv

Rr

τr,t= ∆T

cD

XcD,r,t

XcD,r,t +Xs

D,r,t

+ ∆TcR

XcR,r,t

XcR,r,t +Xs

R,r,t

+ δr +12∑m=1

%mr,t + ωr,t (16)

Here the δr are race fixed effects. These will capture any unobservable systematic differences

that are constant within a state or within an election year, such as the state’s average

ideology, or any specific features of a given electoral year such as the party in power, or

whether it is a midterm election year. As such, we exploit exclusively within-race variation in

media reporting and electoral support changes along the campaign trail. The %mr,t are month-

of-the-year fixed effects. These are important in this setting because the sports events we

32

use as instruments are highly seasonal. As a robustness exercise, we also estimate equation

(16) above with a full set of state, year, and state-x-year fixed effects instead of race fixed

effects.

Estimation of equation (16) requires instruments that vary across poll-to-poll intervals

within a race, for both right-hand side regressors. As mentioned above, we rely on the occur-

rence of major sports events. More specifically, we compute our instruments zlr,t as the fan-

weighted log number of games per day from sports league l ∈ {NFL,MLB,NBA,NCAA}relevant to state r falling within the poll-to-poll interval t:

zlr,t = log

[1

τr,t

∑j

wlrjlr,t

]

where the wlrj are the fraction of state r’s population in counties where a plurality of Facebook

users are fans of a team from state j playing in sports league l. We do not use the Facebook

fan weights for NCAA games (see section 4.4). This amounts to making the wNCAArj = 0 if

r 6= j, and wNCAArr = 1.17

Table 4 presents our main estimates of equation (16) together with the coefficients on

our four instruments in each of the two first stages. Recall that our model predicts that the

occurrence of sports events, by lowering the profitability of campaign reporting, should lead

to an increase in core-targeted reported statements relative to total reported statements.

Reassuringly, there is a systematically positive first-stage relationship between our instru-

ments and each endogenous right-hand side variable in the main equation.18 The first stage

diagnostic statistics reveal that sports events are jointly good predictors of the fraction of

core-targeted to total news articles on a candidate.

Table 4 reports estimates based on the 2-week poll-to-poll interval dataset in the first

four columns, and on the 3-week poll-to-poll interval dataset in the last four columns. In

both cases we report results using the ±0.25 article score cutoff classification described in

section 4.3. We also present estimates from OLS models which illustrate the importance of

appropriately controlling for the endogeneity of equilibrium news coverage. Columns (1), (2),

(5) and (6) present results that include race fixed effects, while columns (3), (4), (7) and (8)

present results that include the state, year, and state-x-year fixed effects instead. In practice,

results are unchanged when using either set of fixed effects. The standard errors we present

throughout allow for heteroskedasticity and serial autocorrelation of up to order two, which

17As additional robustness exercises available upon request, we estimated our main equations using thenumber of winning games per day as instruments instead. Results are very similar.

18The partial correlation coefficient for NCAA games on the first stage forXc

R,r,t

XcR,r,t+X

sR,r,t

is negative.

Nevertheless, the unconditional correlation (without controlling for the remaining sports) is positive.

33

Electoral Share Response Elasticities (0.25 score cutoff)

Panel A: Structural equation Dependent variable: (∆VD + ∆VR)/τ


Explanatory variable Param. OLS 2SLS OLS 2SLS OLS 2SLS OLS 2SLS(1) (2) (3) (4) (5) (6) (7) (8)

RcD/(RcD +RsD) ∆T

cD 0.024 0.16 0.026 0.16 0.032 0.15 0.032 0.18(0.006) (0.06) (0.006) (0.06) (0.006) (0.08) (0.07) (0.089)

RcR/(RcR +RsR) ∆T

cR −0.003 0.05 −0.003 0.05 −0.005 0.09 −0.004 0.09(0.005) (0.058) (0.005) (0.059) (0.005) (0.08) (0.005) (0.088)

Panel B: First Stages Dependent variable: RcD/(RcD +RsD)

Log NFL games/τ 0.076 0.077 0.104 0.119(0.034) (0.035) (0.041) (0.041)

Log MLB games/τ 0.049 0.048 0.034 0.032(0.024) (0.025) (0.026) (0.027)

Log NBA games/τ 0.060 0.060 0.058 0.058(0.020) (0.020) (0.022) (0.022)

Log NCAA games/τ 1.112 1.135 0.695 0.722(0.588) (0.590) (0.674) (0.685)

R2 0.95 0.95 0.96 0.95F test (p-value) 0.001 0.001 0.006 0.003

Dependent variable: RcR/(RcR +RsR)

Log NFL games/τ 0.088 0.089 0.033 0.014(0.034) (0.034) (0.041) (0.042)

Log MLB games/τ 0.087 0.086 0.048 0.050(0.024) (0.024) (0.026) (0.027)

Log NBA games/τ 0.023 0.023 −0.010 −0.012(0.020) (0.020) (0.022) (0.022)

Log NCAA games/τ −1.234 −1.234 −1.339 −1.352(0.579) (0.579) (0.673) (0.688)

R2 0.93 0.93 0.94 0.94F test (p-value) 0.000 0.000 0.05 0.042

Race fixed effects Y Y N N Y Y N NYear×State fixed effects N N Y Y N N Y Y

No. of Races 415 415 415 415 415 415 415 415No. of Observations 2134 2134 2134 2134 1865 1865 1865 1865

Table 4: Turnout Support Gain Elasticities (0.25 score cutoff). The table presents OLS and 2SLSestimates of the turnout gain elasticities from equation (16) using a 0.25 article score cutoff. Even-numberedcolumns present OLS estimates and odd-number columns present 2SLS estimates. Panel A present estimatesfor the structural equation (second stage), and panel B presents estimates of the coefficients for the instru-ments in both the first stages for the Democratic and the Republican ratios of turnout-targeted to total newsreports. The first four columns in the table are estimated on the 2-week poll-to-poll interval panel. The lastfour columns are estimated on the 3-week poll-to-poll interval panel. All regressions are weighted by thesquare root of the length in days of the poll-to-poll interval (relative to the longest interval). Columns (1),(2), (5), and (6) include Senate-race fixed-effects. Columns (3), (4), (7), and (8) include a full set of year,state, and year-x-state fixed effects. All models include a dummy variable for the last poll-to-poll interval ina race and month fixed effects. Standard errors are robust to arbitrary heteroskedasticity and to arbitraryserial correlation of up to order 2 following Newey and West (1987). Coefficients and standard errors inPanel A are multiplied by 1000.

34

we believe is important given the nature of our data. Because we measure the end-of-period

electoral support for the last poll-to-poll interval of each race using the election outcome

instead of a poll, we additionally include a dummy variable for the last poll-to-poll interval

in each race. All of our estimated regressions are also weighted by the square root of the

length in days of the poll-to-poll interval because longer intervals contain more information

than shorter ones and there is significant variation in poll-to-poll interval sizes in our data.

All of our IV estimates for the Democratic turnout elasticity ∆TcD are positive and signifi-

cant. Although the IV estimates for the Republican turnout elasticity ∆TcR are systematically

positive across all of our specifications and robustness exercises, they are significantly smaller

than the Democratic turnout elasticity, and their standard errors are large. This is not too

surprising given the large amount of measurement error in our dependent variable, which

relies on arguably quite noisy polls. Our estimates are also very similar when using the

2-week and the 3-week poll-to-poll intervals. We believe this first result is important, as it

points out that Republican core supporters are much less responsive on the turnout margin

to campaigning targeted towards them than Democratic core supporters. This may be be-

cause solidly Republican constituencies exhibit high baseline turnout rates. It is well known,

for example, that senior white males in rural areas, who tend to favor the Republican party,

turn out at much higher rates than other demographic groups. As a result, Republican

candidates’ incentives to target those sectors of the electorate may be weaker. Democratic

campaigns, in contrast, often appear focused on mobilizing turnout among younger and mi-

nority demographic groups, possibly because these groups have lower average turnout rates,

making the potential gains on this margin large.

Our estimates from Table 4 are informative about the partial equilibrium quantitative

effects of candidate behavior on poll changes. In the bottom panel of Table 6 we report

the average estimates of candidates’ mixing strategies qp, as measured by the ratio of core-

targeted news reports to all news reports. Based on the 0.25 article score cutoff criterion,

E[qD] ≈ 0.56, and E[qR] ≈ 0.45. A ten percent increase in these probabilities, which is

within the range of variation induced by the sports events, if sustained during a month

would translate, on average, into a 3.3 percentage point gain to the Democratic candidate,

and a 0.8 percentage point gain to the Republican candidate stemming from their core

supporters’ increased turnout.19 Because the margin of victory for most Senate races is

around 5 percentage points, this simple exercise illustrates the importance of media coverage

incentives on election outcomes.

With our estimates for (∆TcD,∆

TcR) at hand, we then construct Dr,t and Rr,t as defined in

19(0.1× 0.56)× (0.16/1000)× 124 media outlets on average× 30 days ≈ 0.033 for Democrats, and (0.1×0.45)× (0.05/1000)× 124 media outlets on average× 30 days ≈ 0.008 for Republicans.

35

Proposition 3. We then estimate the swing voter effects of swing voter-targeted candidate

speech by 2SLS using the specification:

Dr,t − Rr,t

2τr,t = ∆S

sD[XcD,r,t +Xs

D,r,t]−∆SsR[Xc

R,r,t +XsR,r,t] + δr +

12∑m=1

%mr,t + ζr,t (17)

Once again, the δr are race fixed effects, and %mr,t are month-of-the-year fixed effects. Recall

from Proposition 3, that through the lens of our model, the regressors in equation (17) are

the sample analogues of τηp(1−γ∼p). Total observed news reports on a candidate should not

vary as a function of changes in the media’s payoff –from equations (3)-(4), these conditional

probabilities only depend on candidates’ payoffs–. Our model suggests that a media outlet’s

reporting strategy is pinned down by indifference, and thus, is independent of its own payoff.

Nevertheless, for the distribution of media outlets as a whole, a shift in the profitability of

reporting on political campaigns can lead to an extensive margin response by outlets entering

into or dropping out from coverage (see Figure 6). Following this idea, we use sports events

as exogenous sources of variation for the two endogenous regressors in equation (17). In this

case, the model predicts sports events should be negatively correlated with [Xcp,r,t + Xs

p,r,t].

This is exactly the pattern we find in the first stage estimates, which we present in Table 5.

Table 5 presents our benchmark estimates of equation (17). The table has the same

structure as that of Table 4. Its first four columns are based on the 2-week poll-to-poll interval

dataset, and the last four are based on the 3-week poll-to-poll interval dataset. All models in

the table are also based on the ±0.25 article score cutoff classification. As discussed above,

the first stage estimates in panel B show that our instruments are systematically negatively

correlated with both the Democratic and the Republican total news reports counts. Panel A

then presents our main estimates of the Democratic and Republican swing-voter elasticities

in response to swing voter-targeted media contents. Quite reassuringly, across all models

estimated by 2SLS we obtain a positive coefficient on [XcD,r,t +Xs

D,r,t] corresponding to ∆SsD,

and a negative coefficient on [XcR,r,t + Xs

R,r,t] corresponding to −∆SsR, exactly as implied by

equation (17). We consider this pattern of resulting signs to very strongly suggest the validity

of our proposed model. The IV estimates in the table show that the swing voter electoral

support elasticities are remarkably similar in magnitude for Democratic and Republican

candidates. Column (4), for example, shows our estimates for both parameters to be 0.0018,

although the one for the Democratic candidate is more precisely estimated. Both ∆SsD

and ∆SsR are significant at the 5% level. Across specifications both the magnitudes and

significance of the parameter estimates are very similar.

We can undertake a quantitative exercise based on our benchmark estimates of (∆SsD,∆

SsR)

36

Electoral Share Response Elasticities (0.25 score cutoff)

Panel A: Structural equation Dependent variable: τ(D − R)/2


Explanatory variable Param. OLS 2SLS OLS 2SLS OLS 2SLS OLS 2SLS(1) (2) (3) (4) (5) (6) (7) (8)

RcD +RsD ∆SsD 0.15 0.18 0.15 0.18 0.15 0.2 0.15 0.2

(0.04) (0.09) (0.04) (0.087) (0.3) (0.10) (0.03) (0.10)

RcR +RsR −∆SsR −0.08 −0.18 −0.08 −0.18 −0.10 −0.27 −0.10 −0.29

(0.02) (0.10) (0.02) (0.11) (0.02) (0.136) (0.02) (0.14)

Panel B: First Stages Dependent variable: RcD/(RcD +RsD)

Log NFL games/τ 1.73 1.08 19.47 18.30(24.07) (24.05) (30.50) (30.48)

Log MLB games/τ −34.72 −34.62 −36.12 −36.00(17.06) (17.06) (19.58) (19.59)

Log NBA games/τ −12.82 −12.82 −17.99 −19.60(13.93) (13.93) (16.43) (16.45)

Log NCAA games/τ −1322.8 −1321.3 −1348 −1347.5(410.13) (410.02) (503.09) (504.2)

R2 0.70 0.70 0.72 0.72F test (p-value) 0.007 0.007 0.029 0.028

Dependent variable: RcR/(RcR +RsR)

Log NFL games/τ −34.52 −34.44 −28.01 −29.04(12.93) (12.92) (16.24) (16.19)

Log MLB games/τ −6.99 −7.02 −7.35 −6.77(9.16) (9.17) (10.42) (10.41)

Log NBA games/τ −22.17 −22.13 −31.59 −31.88(7.49) (7.48) (8.75) (8.74)

Log NCAA games/τ −663.0 −663.8 −582.2 −581.7(220.34) (220.31) (267.91) (267.84)

R2 0.73 0.73 0.76 0.76F test (p-value) 0.000 0.000 0.000 0.000

Race fixed effects Y Y N N Y Y N NYear×State fixed effects N N Y Y N N Y Y

No. of Races 415 415 415 415 415 415 415 415No. of Observations 2134 2134 2134 2134 1865 1865 1865 1865

Table 5: Swing-Voter Gain Elasticities (0.25 score cutoff). The table presents OLS and 2SLS esti-mates of the swing-voter gain elasticities from equation (17) using a 0.25 article score cutoff. Even-numberedcolumns present OLS estimates and odd-number columns present 2SLS estimates. Panel A presents esti-mates for the structural equation (second stage), and panel B presents estimates of the coefficients for theinstruments in both the first stages for the Democratic and the Republican total news reports. The first fourcolumns in the table are estimated on the 2-week poll-to-poll interval panel, and the dependent variable isconstructed using the parameter estimates from the model in Panel A, column (4) of Table 4. The last fourcolumns are estimated on the 3-week poll-to-poll interval panel, and the dependent variable is constructedusing the parameter estimates from the model in Panel A, column (8), of Table 4. All regressions areweighted by the square root of the length in days of the poll-to-poll interval (relative to the longest interval).Columns (1), (2), (5), and (6) include Senate-race fixed-effects. Columns (3), (4), (7), and (8) include a fullset of year, state, and year-x-state fixed effects. All models include a dummy variable for the last poll-to-pollinterval in a race and month fixed effects. Standard errors are robust to arbitrary heteroskedasticity andto arbitrary serial correlation of up to order 2 following Newey and West (1987). Coefficients and standarderrors in Panel A are multiplied by 100. 37

Electoral Share Response Elasticities and Equilibrium Mixing Strategies

Dependent variable: 2 week poll-to-poll intervals

0.25 article score cutoff 0.5 article score cutoff(1) (2)

Panel A Parameters

∆TcD 0.016 0.011

∆TcR 0.005 0.004

∆SsD 0.18 0.12

∆SsR 0.18 0.15

∆ScD 0.69 0.50

∆ScR 0.18 0.15

Panel B Average Equilibrium Mixing Strategies

E[qD] 0.557 0.414

E[qR] 0.449 0.299

E[ηD(1− γR)] 0.018 0.018

E[ηR(1− γD)] 0.014 0.014

Table 6: Identified Parameter Estimates and Equilibrium Mixing Strategies. The table presents allthe identified parameters (Panel A) and average equilibrium mixing probabilities (Panel B) in the modelestimated using the 2-week poll-to-poll interval dataset. Electoral gain elasticities in Panel A are taken fromthe estimation of equations (16) and (17). Swing-voter loss elasticity parameters are computed according toequation (18) in the text. Column (1) is based on the 0.25 article score cutoff and the estimates in column(4) of Table 4 and column (4) of Table 5. Column (2) is based on analogous models using the 0.5 articlescore cutoff. Estimates in Panel B are computed directly from the sample analogues as weighted averagesusing relative interval lengths as weights. Parameter estimates reported in Panel A are multiplied by 100.

similar to the one we discussed above for (∆TcD,∆

TcR). In the bottom panel of Table 6 we

report the average estimates of the unconditional probabilities of observing a news piece,

ηp(1−γ∼p), as measured by the ratio of observed news pieces relative to the number of relevant

stage games. Based on the 0.25 article score cutoff criterion, E[ηD(1 − γR)] ≈ 0.018, and

E[ηR(1−γD)] ≈ 0.014. A ten percent increase in these probabilities sustained during a month

would translate, on average, into a 1.2 percentage point gain to the Democratic candidate,

and a 1 percentage point gain to the Republican candidate, stemming from increased swing

voter support. These would be losses for the opposing candidate20.

20(0.1× 0.018)× (0.18/100)× 124 media outlets on average× 30 days ≈ 0.012 for Democrats, and (0.1×0.014)× (0.18/100)× 124 media outlets on average× 30 days ≈ 0.010 for Republicans.

38

The next step in our empirical strategy is to back out estimates of the swing voter

responses to core-targeted campaign speech using the equilibrium mixing strategies of the

media in equations (3)-(4), together with our estimates φp of the conditional reporting proba-

bilities ηp(1−γ∼p) as described in Proposition 3. We obtain average elasticities by integrating

over our sample as follows:

∆Scp =

∆Tcp

1N

∑r

∑Trt=1 φp,r,t

− ∆Ssp (18)

Panel A in Table 6 presents the estimates of all six poll-change elasticities in our model.

The table presents estimates using the 2-week poll-to-poll interval dataset, both using the

±0.25 article cutoff classification in column (1), and the ±0.5 cutoff in column (2). The

magnitude of the estimates is very similar for both cutoffs, showing that the specific criterion

chosen to classify articles as c or s is not critical for our results. The full set of parameters is

also similar when using the 3-week poll-to-poll intervals. These results are omitted to save

space. As the table illustrates, the swing voter responsiveness to core-targeted statements is

significantly larger for the Democratic candidate than for the Republican candidate. Using

the ±0.25 cutoff estimates, ∆ScD = 0.69, ∆S

cR = 0.18. Our estimates suggest that swing

voters are on average very sensitive to media content that signals relatively core-mobilizing

campaign speech by Democrats. This difference in poll response elasticities across parties has

substantial implications for the dynamics of the Senate races; although the turnout gains of

core-targeted statements are larger for Democrats than for Republicans, the cost on the swing

voter margin is even larger. If both centrist voters and the media play a role in moderating

candidates’ campaign trail speech, these results suggest that swing voters are especially

important in fulfilling this role for Democratic candidates, while the media is relatively more

important to constrain the behavior of Republican candidates. The equilibrium implication

of this pattern of parameters is that candidates from both parties are covered by the media

at similar rates. As we pointed out above, our average estimates for these probabilities,

reported in Panel B of Table 6, are 0.018 for Democrats and 0.014 for Republicans. These

should be understood as the average unconditional probabilities that a given media outlet

generates a news piece on a candidate in a given day during the campaign.

6.2 Payoff Heterogeneity

The 2SLS estimates of the payoff parameters (∆TcD,∆

TcR,∆

SsD,∆

SsR,∆

ScD,∆

ScR) described above

are average effects across states and three decades, identified off the variation in media

coverage and poll changes within races over time. In this section we explore the extent

39

of heterogeneity in these payoff parameters across races. We do so in a straightforward

parametric way by allowing the payoff parameters we recover from equations (16) and (17)

to depend on race characteristics which may be important sources of heterogeneity. Here

we discuss four sources of heterogeneity: the partisan distribution of voters across states

and time, the time to election day, the competitiveness of the election at a given point

in time, and the presence of an incumbent senator in the race. Specifically, we allow the

payoff elasticities to be linear functions of one of these four characteristics Kr,t: ∆Tcp =

αTcp + βTcpKr,t and ∆Ssp = αSsp + βSspKr,t for p ∈ {D,R}.21 We estimate equations (16) and

(17) by 2SLS including the relevant interaction terms, instrumenting the interaction terms

with the respective interactions between our sports events instruments and the source of

heterogeneity in each case.22

6.2.1 The partisan distribution of voters

We first explore heterogeneity in electoral responses as a function of the partisan distribution

of the electorate, which varies considerably across states. We proxy this distribution using the

average of the Democratic registration share of the electorate and the most recent presidential

election results. For states without partisan registration, we use only the presidential election

returns. The results for this exercise are presented in column (1) of Table 7. These and all

other estimates in the table use our benchmark 2-week poll-to-poll interval dataset based

on the ±0.25 article score cutoff and are estimated by 2SLS using all sports events and

interactions of sports events and voter registration as instruments. Panel A presents the

estimates for the turnout elasticities from equation (16), while panel B presents the estimates

for the swing voter elasticities from equation (17). Although the pattern of signs implies

that ∆TcD decreases while ∆T

cR increases with Democratic registration, we cannot estimate

these effects precisely. In contrast, we find a significant decreasing relationship between

Democratic registration and ∆SsD. In states with relatively few Democratic voters, these

21An additional reason to explore heterogeneity in this context is the potential bias of our estimatesif parameters vary substantially over time because we base our empirical strategy on the computation ofprobabilities based on relative frequencies. On the one hand, if the underlying probabilities vary substantiallyover time, the sample analogue estimators of the mixing probabilities will be biased. This would make shorterpoll-to-poll intervals preferable. On the other hand, longer poll-to-poll intervals reduce sampling error, aslong as the ∆’s are constant within a time interval. This is an unavoidable bias-precision trade-off.

22To recover the remaining elasticities ∆Scp(K) when allowing for heterogeneity, we construct decile bins

for Kp,r and compute the integration in equation (18) restricted to the set ΓK = {(r, t) : Kr,t ∈ K} ofobservations falling in each decile:

∆Scp(K) =

∆Tcp(Kp,r)

1|ΓK |

∑r

∑Tr

t=1 φp,r,t− ∆S

sp(Kp,r), (r, t) ∈ ΓK .

40

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(0.0

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41

voters appear to be more responsive to swing-voter targeted media coverage favoring the

Democratic candidates. Except for this result, the partisan distribution of the electorate

does not appear to be a major source of heterogeneity in electoral response elasticities across

states or over time.

6.2.2 Days to Election

In a second exercise we explore the possibility that the electoral responsiveness of voters

varies during the campaign. For example, if voters pay more attention to media coverage as

November approaches, they may become more responsive to the news over time. We explore

this possibility by allowing the payoff parameters in equations (16) and (17) to depend on

the time between the initial date of the poll-to-poll interval and the general election date.

Because the time to election day varies across poll-to-poll intervals within race, we also

include the time to election as a covariate. Our main results for this exercise are presented

in column (2) of Table 7. They show no statistically significant evidence of heterogeneity on

time to election day. Overall, the ∆’s appear to be stable along the campaign trail.

6.2.3 State of the Race: A Dynamic Game

We also explore whether poll response elasticities vary as a function of an endogenous state

variable, making the game in practice a dynamic one rather than a repeated one. It is

possible that both candidates’ and the media’s incentives change along the campaign trail

as a function of the political environment and the previous evolution of the race itself. On

the one hand, we may expect a candidate to become more willing to take risks when he

is behind in the polls. On the other hand, the electoral cost of bad press may grow as

election day approaches, making politicians more cautions late in the race. Similarly, the

media’s campaign coverage profitability may grow as election day approaches. To explore

these possibilities and their implications for the robustness of our results, we allow payoff

parameters to depend on the current state of the race as measured by the poll margin between

candidates at the beginning of the corresponding poll-to-poll interval.23

We now have a dynamic game where payoffs depend on a state variable, and where the

state variable itself evolves over time as a function of the players’ previous choices. Even

in this case, the finite horizon of the game and the uniqueness of Nash equilibrium in its

stage game imply that the dynamic game only has one sub-game perfect equilibrium. It

prescribes playing the mixed-strategy Nash equilibrium of the stage game given the value

23In principle, the relevant state variable may be a high-dimensional vector of time-varying characteristics.In practice, our sample size requires us to limit the dimensionality of the state variable we consider.

42

of the state variable at every period. As a result, equilibrium play is independent across

periods conditional on the state variable, and we can replicate our estimation strategy from

above. Similar to the time-to-election exercise, the poll margin varies over time within a

race, so we also include it separately as a covariate.

Results for this exercise are presented in column (3) of Table 7. Overall, we do not find

a strong relationship between the state of the race and the electoral support elasticities.

The only exception arises for the swing-voter response elasticity to swing-targeted speech for

Republicans, ∆SsR. This parameter is higher in more competitive periods of a race. Taken at

face value, it suggests that incentives to target swing voters become stronger for Republican

candidates as races become closer. The results from this exercise should be taken with

caution because the poll margin is an endogenous outcome which we are including as a

covariate.

6.2.4 Incumbent Running

Our final exercise looking at payoff heterogeneity explores whether poll responsiveness differs

in races where incumbents are running. We allow the ∆’s to depend on a dummy variable

for elections with a running incumbent. Results for this exercise are presented in column

(4) of Table 7. We find no evidence of differences in candidate payoff parameters in races

with or without incumbents. We should notice, however, that this test may not have much

power: 75% of all Senate races in our sample have an incumbent running.

6.3 Robustness Exercises and Specification Tests

6.3.1 Robustness Exercises

In Tables 8 and 9 we present a subset of additional econometric exercises exploring the

robustness of our main findings. Table 8 reports 2SLS results for alternative specifications

based on the 2-week poll-to-poll interval dataset. First, we estimate equations (16)-(17)

excluding the last poll-to-poll interval for each race. We do this for two reasons. First,

our last poll-to-poll interval for each race is constructed using the general election result

as the end-of period value. This is in contrast to all other periods in which beginning and

end-of-period electoral support are measured using averages of polls. Second, the validity

of our instruments relies on the assumption that sports events are shifters of the media’s

reporting payoffs, but do not otherwise affect the evolution of the polls. If sports events that

happen very near election day –thus falling on the last poll-to-poll interval– directly lead to

lower turnout in elections, the exclusion restriction would not be satisfied.24 Excluding these

24We believe this is unlikely given that poll-to-poll intervals cover an average of 30 days.

43

Robustness exercises (2 week poll-to-poll intervals)

Robustness exercise:

Panel A Excluding lastpoll-to-poll

interval

Controlling forpost-primary

dummy

0.5 article scorecutoff

0.75 articlescore cutoff

Parameter Regressor (1) (2) (3) (4)

Dependent variable: (∆VD + ∆VR)/τ

∆TcD RcD/(R

cD +RsD) 0.015 0.014 0.011 0.015

(0.005) (0.005) (0.005) (0.006)

∆TcR RcR/(R

cR +RsR) 0.003 0.008 0.004 0.005

(0.005) (0.006) (0.005) (0.006)

Panel B Dependent variable: τ(D − R)/2

∆SsD RcD +RsD 0.21 0.13 0.12 0.12

(0.08) (0.056) (0.056) (0.06)

−∆SsR RcR +RsR −0.24 −0.16 −0.15 −0.14

(0.12) (0.082) (0.076) (0.078)

No. of races 415 415 415 415No. of observations 1871 2134 2134 2134

Table 8: Robustness Exercises. The table presents 2SLS estimates of the electoral support elasticitiesfrom equations (22) and (23). All models are estimated on the 2 week poll-to-poll interval panel, andinclude a full set of Senate-race fixed effects, and month fixed effects. The dependent variable in Panel Bis constructed using the parameter estimates from Panel A. All regressions are weighted by the square rootof the length in days of the poll-to-poll interval (relative to the longest interval). Column (1) excludes allobservations consisting of the last poll-to-poll interval in a race. Columns (2), (3), and (4) include a dummyvariable for the last poll-to-poll interval in a race. All models use log of NFL games per day, log of MLBgames per day, log of NBA games per day, and log of NCAA games per day as instruments. Standarderrors are robust to arbitrary heteroskedasticity and to arbitrary serial correlation of up to order 2 followingNewey and West (1987). Coefficients and standard errors in Panels A and B are multiplied by 100.

44

observations reduces the sample size from 2134 to 1871. As column (1) in Table 8 shows,

the magnitude and significance of the estimated parameters is almost unchanged relative to

our baseline estimates.

In column (2) we then include a dummy variable for poll-to-poll intervals after the primary

election for the race. If the strategic environment is significantly different before and after the

primaries have taken place, it may be important to distinguish between both regimes. For

most races, even during primary campaign days, pollsters are already collecting polls asking

for the candidates who eventually become the Democratic and Republican nominees. This

suggests that in most cases, the bipartisan race is already implicitly taking place before the

primary outcome is known. As column (2) in Table 8 shows, controlling for a post-primary

dummy variable does not alter any of our benchmark estimates either.

Finally, in columns (3) and (4) of Table 8 we estimate our main specification using two

alternative article score cutoffs. Column (3) presents estimates using a ±0.5 cutoff, and

column (4) presents estimates using a quite extreme ±.75 cutoff. Because our classification

cutoff for core-targeted versus swing-targeted news content is arbitrary, it is reassuring that

our main results are unaltered.

In Table 9 we turn to a sensitivity analysis of our estimates to the inclusion of alternative

subsets of our sports events instruments. These, in practice, amount to over-identification

exercises. We report the results from models using the 2-week (columns (1)-(5)) and the

3-week (columns (6)-(10)) poll-to-poll interval datasets, using the ±0.25 article score cutoff

classification. Panel AI presents the parameter estimates for equation (16). Panel BI presents

the parameter estimates for equation (17). Panels AII and BII present diagnostic statistics

for the respective first stages that include different subsets of instruments. We present results

that omit one by one each of the four sports events from the instrument set in columns (1)-

(4) and (6)-(9). In columns (5) and (10) we also include a more demanding specification

where we omit both MLB and NBA games simultaneously, making these models exactly

identified. The F-tests for the excluded instruments across the table do suggest that we

lose some of the joint predictive power of our instruments when excluding some of them.

However, we fail to reject the null of no joint significance in only 4 out of the 40 first stages

reported in the Table. Standard errors for the parameter estimates are also somewhat larger,

but in most cases the parameter estimates that are significant in our benchmark specification

using all instruments remain significant at the 5% level when using only a subset of them.

More importantly, the table shows that the magnitude and pattern of signs for the estimated

parameters remain unchanged relative to our baseline model estimates.

45

Over

iden

tifica

tion

Exer

cise

s

2w

eek

pol

l-to

-pol

lin

terv

als

3w

eek

poll-t

o-p

oll

inte

rvals

Excl

uded

Inst

rum

ents

:N

FL

ML

BN

BA

NC

AA

ML

B,

NB

AN

FL

ML

BN

BA

NC

AA

ML

B,

NB

AP

anel

AI:

Str

uct

ura

lE

quat

ion

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

Reg

ress

orP

aram

.D

epen

den

tva

riab

le:

(∆VD

+∆VR

)/τ

Rc D/(Rc D

+Rs D

)∆T cD

0.01

40.

019

0.01

10.

024

0.01

50.

009

0.0

18

0.0

20

0.0

20.0

21

(0.0

06)

(0.0

08)

(0.0

06)

(0.0

10)

(0.0

09)

(0.0

07)

(0.0

10)

(0.0

10)

(0.0

07)

(0.0

12)

Rc R/(Rc R

+Rs R

)∆T cR

0.00

30.

013

0.00

40.

000.

013

0.00

50.0

013

0.0

09

0.0

10.0

12

(0.0

06)

(0.0

10)

(0.0

04)

(0.0

1)(0

.009

)(0

.007

)(0

.012)

(0.0

08)

(0.0

1)

(0.0

12)

Pan

elA

II:

Fir

stSta

ges

Dep

enden

tva

riab

le:Rc D/(Rc D

+Rs D

)

R2

0.78

0.78

0.78

0.78

0.78

0.80

0.8

00.8

00.8

00.8

0F

test

(p-v

alue)

0.01

40.

011

0.05

80.

011

0.03

70.

071

0.0

15

0.0

82

0.0

14

0.0

42

Dep

enden

tva

riab

le:Rc R/(Rc R

+Rs R

)

R2

0.80

0.80

0.80

0.80

0.80

0.82

0.8

20.8

20.8

20.8

2F

test

(p-v

alue)

0.00

20.

076

0.00

00.

001

0.03

20.

021

0.0

67

0.0

19

0.1

66

0.0

53

Pan

elB

I:Str

uct

ura

lE

quat

ion

Reg

ress

orP

aram

.D

epen

den

tva

riab

le:τ(D−R

)/2

Rc D

+Rs D

∆S sD

0.10

0.24

0.18

0.10

0.30

0.12

0.2

70.1

90.1

50.3

2(0

.07)

(0.1

0)(0

.08)

(0.1

1)(0

.14)

(0.0

7)(0

.11)

(0.0

9)

(0.1

2)

(0.1

7)

Rc R

+Rs R

−∆S sR

−0.

02−

0.21

−0.

20−

0.19

−0.

33−

0.15

−0.3

0−

0.2

9−

0.2

7−

0.4

6(0

.16)

(0.1

1)(0

.12)

(0.1

1)(0

.17)

(0.0

13)

(0.1

4)

(0.1

7)

(0.1

2)

(0.2

8)

Pan

elB

II:

Fir

stSta

ges

Dep

enden

tva

riab

le:Rc D

+Rs D

R2

0.60

0.60

0.60

0.60

0.60

0.63

0.6

30.6

30.6

30.6

3F

test

(p-v

alue)

0.06

20.

095

0.04

60.

495

0.04

70.

090

0.1

34

0.0

88

0.6

72

0.0

62

Dep

enden

tva

riab

le:Rc R

+Rs R

R2

0.60

0.60

0.60

0.60

0.60

0.64

0.6

40.6

40.6

40.6

4F

test

(p-v

alue)

0.00

90.

001

0.00

30.

013

0.00

10.

016

0.0

06

0.0

48

0.0

37

0.0

23

No.

ofra

ces

415

415

415

415

415

415

415

415

415

415

No.

ofob

serv

atio

ns

2134

2134

2134

2134

2134

1865

1865

1865

1865

1865

Tab

le9:

Ove

rid

enti

fica

tion

Exer

cise

s.T

he

tab

lep

rese

nts

2SL

Ses

tim

ates

ofth

eel

ecto

ral

sup

por

tel

asti

citi

esfr

omeq

uat

ion

s(1

6)in

Pan

elA

,an

d(1

7)in

Pan

elB

.A

llm

od

els

are

esti

mat

edu

sin

gth

e0.

25ar

ticl

esc

ore

cuto

ff,

and

incl

ud

ea

full

set

ofS

enat

e-ra

cefi

xed

effec

ts,

mon

thfi

xed

effec

ts,

an

da

du

mm

yva

riab

lefo

rth

ela

stp

oll-

to-p

oll

inte

rval

ina

race

.T

he

dep

end

ent

vari

able

for

the

stru

ctu

ral

equ

atio

nin

Pan

elB

Iis

con

stru

cted

usi

ng

the

ben

chm

ark

par

amet

eres

tim

ates

from

the

stru

ctu

ral

equ

atio

n(1

6).

Col

um

ns

(1)-

(5)

are

bas

edon

the

esti

mat

efr

omco

lum

n(4

)of

Tab

le4.

Colu

mn

s(6

)-(1

0)ar

eb

ased

onth

ees

tim

ate

from

colu

mn

(8)

inT

able

4.P

anel

sA

Ian

dB

Ip

rese

nt

esti

mat

esfo

rth

est

ruct

ura

leq

uat

ion

s(s

econ

dst

ages

),an

dP

anel

sA

IIan

dB

IIre

por

tth

eco

rres

pon

din

gR

-squ

ared

and

p-v

alu

efo

rth

eF

-tes

tson

the

excl

ud

edin

stru

men

tsfo

rea

chfi

rst

stag

e.T

he

dep

end

ent

vari

able

sin

the

firs

tst

age

sof

Pan

elA

IIar

eth

eD

emocr

atic

and

Rep

ub

lica

nra

tios

oftu

rnou

t-ta

rget

edto

tota

ln

ews

rep

orts

.T

he

dep

end

ent

vari

ab

les

inth

efi

rst

stag

esof

Pan

elB

IIar

eth

eD

emocr

atic

and

Rep

ub

lica

nto

tal

new

sre

por

ts.

Th

efi

rst

five

colu

mns

inth

eta

ble

are

esti

mat

edon

the

2w

eek

pol

l-to

-pol

lin

terv

alp

anel

.T

he

last

five

colu

mn

sar

ees

tim

ated

onth

e3

wee

kp

oll-

to-p

oll

inte

rval

pan

el.

All

regr

essi

ons

are

wei

ghte

dby

the

squ

are

root

ofth

ele

ngth

ind

ays

ofth

ep

oll-

to-p

oll

inte

rval

(rel

ativ

eto

the

lon

gest

inte

rval

).C

olu

mn

s(1

)an

d(6

)ex

clu

de

the

log

nu

mb

erofNFL

gam

esp

erd

ayfr

omth

ein

stru

men

tse

t.C

olu

mn

s(2

)an

d(7

)ex

clu

de

the

log

nu

mb

erofMLB

gam

esp

erd

ayfr

omth

ein

stru

men

tse

t.C

olu

mn

s(3)

an

d(8

)ex

clu

de

the

log

nu

mb

erofNBA

gam

esp

erd

ayfr

omth

ein

stru

men

tse

t.C

olu

mn

s(4

)an

d(9

)ex

clu

de

the

log

nu

mb

erofNCAA

gam

esp

erd

ayfr

om

the

inst

rum

ent

set.

Col

um

ns

(5)

and

(10)

pre

sent

aju

st-i

den

tifi

edm

odel

excl

ud

ing

the

log

nu

mb

erofMLB

gam

esp

erd

ayan

dth

elo

gnu

mb

erof

NBA

gam

esp

erd

ayfr

om

the

inst

rum

ent

set.

Sta

nd

ard

erro

rsar

ero

bu

stto

arb

itra

ryh

eter

osked

asti

city

and

toar

bit

rary

seri

alco

rrel

ati

on

of

up

toor

der

2fo

llow

ing

New

eyan

dW

est

(198

7).

Coeffi

cien

tsan

dst

and

ard

erro

rsin

Pan

els

AI

and

BI

are

mu

ltip

lied

by

100.

46

Testing Model Assuptions: Poll Timing and Race Tightness

Dependent variable: Polls in poll-to-poll intervalPolls in poll-to-poll interval

Length of poll-to-poll interval

Poll-to-poll interval size: 2 week 3 week 2 week 3 week(1) (2) (3) (4)

Race tightness (|VD − VR|) 0.041 0.100 0.001 0.025(0.506) (0.697) (0.066) (0.077)

R2 0.39 0.48 0.42 0.47No. of Races 415 415 415 415No. of Observations 2134 1865 2134 1865

Table 10: Testing Model Assumptions: Poll Coverage Intensity and Race Competitiveness: Thetable presents OLS panel regressions of a measure of poll coverage intensity on the tightness of the Senate raceas measured by the absolute value of the difference between the Democratic candidate’s electoral supportand the Republican candidate’s electoral support. The dependent variable in columns (1) and (2) is thenumber of polls in the poll-to-poll interval. The dependent variable in columns (3) and (4) is the numberof polls per day in the poll-to-poll interval. All models include a full set of Senate-race fixed effects, monthfixed effects, a dummy variable for the last poll-to-poll interval in a race, and a constant. All regressions areweighted by the square root of the length in days of the poll-to-poll interval (relative to the longest interval).Standard errors are robust to arbitrary heteroskedasticity.

6.3.2 A Test for Poll Timing Independence

Finally, we are also able to indirectly test whether the timing of polls appears to be uncor-

related with the evolution of the Senate races. Recall from our discussion in section 4.2 that

this underlies the validity of our method for building the poll-to-poll intervals which deter-

mine the panel structure of our dataset. We do this by exploring the correlation between

the frequency of actual polls in our dataset and the competitiveness of the race at any given

point in time. In Table 10 we report results from OLS regressions of the number of actual

polls used to construct the average end-poll of each poll-to-poll interval, on the measure

of race competitiveness we introduced in section 6.2. We present results with or without

normalizing by the length of the interval in days, and for both the 2-week and the 3-week

poll-to-poll interval datasets. As the table illustrates, we find no correlation between poll

frequencies and the state of the race. Pollsters do not appear to be releasing polls as a func-

tion of how the race is evolving. We see these results, together with those using alternative

poll-to-poll windows, as reassuring.

6.4 Partial Identification of the Media Reporting Biases

We conclude the discussion of our empirical findings showing that the media’s partisan

reporting biases are only partially identified in our model. We then compute their identified

set.

47

0.00 0.05 0.10 0.15 0.20ΗD0.00

0.05

0.10

0.15

0.20ΗR

Figure 7: Identified set for media biases (ηD, ηR).

Although our identification strategy allows us to recover all of the payoff parameters

governing the poll change technology (∆TcD,∆

TcR,∆

ScD,∆

ScR,∆

SsD,∆

SsR) and the conditional

probabilities of a media report (ηp(1 − γ∼p)), we cannot separately identify the ηp’s from

the γp’s. The reason is that observed counts of reports are the outcome of both media

coverage and successful reporting, and these events are indistinguishable based on observed

news reports alone. In equilibrium, observed media reporting on a given candidate results

from the interaction between the reporting bias and the media’s mixed strategy. Our model

does provide, however, additional structure to partially identify the ηp’s (and thus the γp’s

through equations (3)-(4)). Equation (11) directly allows us to solve for γp as a function

of the media bias for the opposing candidate η∼p, and the reduced form parameter φ∼p:

γp = 1 − 1η∼p

φ∼p. Because γp ∈ (0, 1), it follows that ηD > φD and ηR > φR. Furthermore,

γD + γR < 1 implies that

ηR <φR

1− 1ηDφD

(19)

These three inequalities determine the identified set for (ηD, ηR), which we illustrate in Fig-

ure 7 at our benchmark estimates for (φD, φR). The hyperbola represents the constraint

in the right-hand side of equation 19.25 As Figure 7 illustrates, our estimates restrict con-

25Notice that we can exploit the candidates’ equilibrium mixing probabilities from equations (5)-(6) to-gether with our identified set for the ηp’s to obtain an identified set for the relative payoff to the media fromreporting about R and D:

πRπD

=ηDηR

q∗Dq∗R

48

siderably the range of values that the ηp’s can take. In particular, the region over which

very asymmetric values for ηD and ηR are feasible is very small. For example, if we were to

consider a uniform prior over this identified set, most of the density would fall over a region

where ηD is close in magnitude to ηR. This is the basis of our assertion that a large media

bias as measured by a large difference in the ηp’s across parties is very unlikely.

7 Concluding Remarks

In this paper we develop a framework to study how the interaction between the media’s

incentives to cover and report on electoral campaigns, and candidates’ incentives to target

different groups of voters, shape both campaign trail speech, and the evolution of the races

themselves. We do this by proposing a simple game-theoretic model of the interaction

between the media and candidates, where the media gains from reporting on core-supporter

targeted campaign speech from candidates, while candidates benefit from reports about

swing voter-targeted messages. Because candidates have incentives to target both types of

constituencies, this strategic environment is similar to a standard matching pennies game.

The simple structure of the game allows us to propose an empirical strategy to estimate

this discrete game of complete information, and to test for its empirical relevance. We do so

using information on U.S. Senate races from the last 30 years, which are politically salient

and thus, systematically covered by the media and by pollsters. We show how polling data

measuring the evolution of the campaigns, together with media coverage information based

on a text analysis methodology, can be used to estimate the key parameters of the game. Our

results suggest the mechanism we propose here is important for understanding the nature of

bipartisan electoral competition in settings with ample media presence. Moreover, our model

and results provide a novel way of thinking about how and why the media matters in politics,

by highlighting not only that the media shapes candidate behavior, but also that candidates

shape the way the media reports about politics. Our empirical findings suggest a large

asymmetry across Democratic and Republican candidates in their incentives to target core

supporters. While turnout appears more responsive to core-targeted speech by Democrats,

swing-voters also appear more willing to change allegiances towards Republicans when the

media reports widely on core-targeted messaging by Democrats. Exploring the nature of the

differential responses of the electorate to targeted campaign messages may be a fruitful area

for future research.

which we can trace on the identified set for (ηD, ηR) at the estimated qp’s. These can be interpreted asbounds on the relative media payoffs from Democratic versus Republican coverage.

49

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51

A Appendix A

A.1 Proof of Proposition 1

The normal form game G is presented in table 11 below. In each cell, the payoffs are written in the order(D,R,M).

Existence and Uniqueness:

Define the following parameters:

41 ≡ ∆TcD − ηD∆S

cD + ηR∆ScR 413 ≡ ∆T

cD − ηD∆ScD − ηR∆S

sR

42 ≡ ∆TcR − ηR∆S

cR + ηD∆ScD 414 ≡ ηR∆S

sR + ηD∆ScD

43 ≡ ∆TcD − ηD∆S

cD 415 ≡ ∆TcD − ηD∆S

cD

44 ≡ ∆TcR + ηD∆S

cD 416 ≡ ηD∆ScD

45 ≡ ∆TcD + ηR∆S

cR 417 ≡ ∆TcD − ηR∆S

sR

46 ≡ ∆TcR − ηR∆S

cR 418 ≡ ηR∆SsR

47 ≡ ηD∆SsD + ηR∆S

cR 419 ≡ ηD∆SsD − ηR∆S

sR

48 ≡ ∆TcR − ηR∆S

cR − ηD∆SsD 420 ≡ ηR∆S

sR − ηD∆SsD

49 ≡ ηD∆SsD 421 ≡ ηD∆S

sD

410 ≡ ∆TcR − ηD∆S

sD 422 ≡ −ηD∆SsD

411 ≡ ηR∆ScR 423 ≡ −ηR∆S

sR

412 ≡ ∆TcR − ηR∆S

cR 424 ≡ ηR∆SsR

G is a game with finite action space, which is sufficient for existence of a Nash equilibrium. Checkingthe non-existence of a Nash equilibrium in pure strategies is straightforward. Thus, any equilibria must bein mixed strategies. Conditions for such an equilibrium are:

1. M must be indifferent between playing aM = FDFR and aM = FDNR:

E[UM |FDFR] = qDqR(ηDπD+ηRπR−2k)+(1−qD)qR(ηRπR−2k)+qD(1−qR)(ηDπD−2k)+(1−qD)(1−qR)(−2k)

Media’s actionaM = FDFR aM = FDNR aM = NDFR

aD = c (∆1,∆2, ηDπD + ηRπR − 2k) (∆3,∆4, nDπD − k) (∆5,∆6, nRπR − k)aR = c

aD = s (∆7,∆8, nRπR − 2k) (∆9,∆10, −k) (∆11,∆12, nRπR − k)Democrat’s Republican’sAction Action

aD = c (∆13,∆14, ηDπD − 2k) (∆15,∆16, nDπD − k) (∆17,∆18, −k)aR = s

aD = s (∆19,∆20, −2k) (∆21,∆22, −k) (∆23,∆24, −k)

Table 11: Normal Form of the Stage Game.

52

= qDqR(ηDπD − k) + (1− qD)qR(−k) + qD(1− qR)(ηDπD − k) + (1− qD)(1− qR)(−k) = E[UM |FDNR]

⇔ q∗R =k

ηRπR(A.1)

2. M must be indifferent between aM = FDFR and aR = NDFR:

E[UM |FDFR] = qDqR(ηDπD+ηRπR−2k)+(1−qD)qR(ηRπR−2k)+qD(1−qR)(ηDπD−2k)+(1−qD)(1−qR)(−2k)

= qDqR(ηRπR − k) + (1− qD)qR(ηRπR − k) + qD(1− qR)(−k) + (1− qD)(1− qR)(−k) = E[UM |NDFR]

⇔ q∗D =k

ηDπD(A.2)

3. D must be indifferent between aD = c and aD = s:

E[UD|c] = (1− γD − γR)qR41 + γDqR43 + γRqR45

+(1− γD − γR)(1− qR)413 + γD(1− qR)415 + γR(1− qR)417

= (1− γD − γR)qR47 + γDqR49 + γRqR411

+(1− γD − γR)(1− qR)419 + γD(1− qR)421 + γR(1− qR)423 = E[UD|s]

⇔ γ∗R = 1− ∆TcD

ηD[∆ScD + ∆S

sD

] (A.3)

4. R must be indifferent between aD = c and aD = s:

E[UR|c] = (1− γD − γR)qD42 + γDqD44 + γRqD46

+(1− γD − γR)(1− qD)48 + γD(1− qD)410 + γR(1− qD)412

= (1− γD − γR)qD414 + γDqD416 + γRqD418

+(1− γD − γR)(1− qD)420 + γD(1− qD)422 + γR(1− qD)424 = E[UR|s]

⇔ γ∗D = 1− ∆TcR

ηR[∆ScR + ∆S

sR

] (A.4)

Thus, the mixed-strategy Nash equilibrium is unique.


Consider taking the difference between the poll outcomes for a candidate between stage games t+ τ and t.From equation (2) across τ stage games, the change in electoral support to candidate p ∈ {D,R} is given by

vp(t+ τ)− vp(t) = ∆TcpN

cp(t, t+ τ) +

(∆Tcp −∆S

cp

)Xcp(t, t+ τ)

+ ∆Sc∼pX

c∼p(t, t+ τ) + ∆S

spXsp(t, t+ τ)−∆S

s∼pXs∼p(t, t+ τ) + εp(t, t+ τ) (A.5)

where εp(t, t + τ) =∑t+τι=t+1 ε

p(ι). Now add together the equations for each candidate, and divide by thenumber of stage games in the interval. The zero-sum nature of swing-voter support implies all swing votereffects cancel out, and we are left with an expression that only depends on the counts of events that generateelectoral responses on the turnout margin:

vD(t+ τ)− vD(t) + vR(t+ τ)− vR(t)

τ=

∆TcD

N cD(t, t+ τ) +Xc

D(t, t+ τ)

τ+ ∆T

cR

N cR(t, t+ τ) +Xc

R(t, t+ τ)

τ+ ω(t, t+ τ) (A.6)

53

where ω(t, t + τ) ≡ εD(t,t+τ)τ + εR(t,t+τ)

τ . This specification cannot be estimated because the (N cD, N

cR) are

unobserved. Even if an instrument z that satisfies the exclusion restriction of being uncorrelated with otherdeterminants of the evolution of electoral support ω is available, it will necessarily be correlated with N c

p aslong as it is correlated with Xc

p. This implies that it is not possible to leave N cD and N c

R in the error term ofequation (A.6) if we want to implement an instrumental variables strategy. Instead, notice that equilibrium

play implies q∗p = Eτ[Nc

p(t,t+τ)+Xcp(t,t+τ)

τ

], and thus, we can express each of the (endogenous and unobserved)

regressors in equation (A.6) as the equilibrium mixing strategy of the candidate plus sampling noise ξp(t, t+τ)that converges in probability to zero at rate

√τ and is uncorrelated with z:

N cp(t, t+ τ) +Xc

p(t, t+ τ)

τ= q∗p(t, t+ τ) +

1

τξp(t, t+ τ)

Now use our non-parametric estimator for q∗p(t, t+ τ) from equations (10) and (11), and define ω(t, t+ τ) ≡ω(t, t + τ) + ∆T

cD1τ ξD(t, t + τ) + ∆T

cR1τ ξR(t, t + τ) as a composite error term that includes all the shocks in

the interval and the sampling error to obtain equation (12).


We first use our non-parametric estimator for the unconditional probability of a media report from equation(11), together with the equilibrium mixing strategies for the media in equations (3) and (4) to express theswing voter elasticities to core-targeted statements for each candidate ∆S

cp as functions only of observables

and the estimated ∆Tcp’s from the estimation of equation (12):

∆Scp =

∆Tcp

φp−∆S

sp (A.7)

Using equation (A.7) we can now eliminate the ∆Scp from equation (A.5) to obtain:

vp(t+ τ)− vp(t)− ∆Tcp[X

cp(t, t+ τ) +N c

p(t, t+ τ)] =(∆Ssp −

∆Tcp

φp

)Xcp(t, t+ τ) +

(∆Tc∼p

φ∼p−∆S

s∼p

)Xc∼p + ∆S

spXsp(t, t+ τ)−∆S

s∼pXsp(t, t+ τ) + εp(t, t+ τ)

Grouping terms,

[vp(t+ τ)− vp(t)]− ∆Tcp[X

cp(t, t+ τ) +N c

p(t, t+ τ)] + ∆Tcp

Xcp(t, t+ τ)

φp− ∆T

c∼pXc∼p(t, t+ τ)

φ∼p=

∆Ssp[X

cp(t, t+ τ) +Xs

p(t, t+ τ)]−∆Ss∼p[X

sp(t, t+ τ) +Xc

∼p(t, t+ τ)] + εp(t, t+ τ)

Multiplying and dividing by τ the second and third terms in the left-hand side of this expression, we havethat

Xcp(t, t+ τ) +N c

p(t, t+ τ)

ττ =

ϕcp(t, t+ τ)

φp(t, t+ τ)τ + ξp(t, t+ τ)

andXcp(t, t+ τ)

φp

τ

τ=ϕcp(t, t+ τ)

φp(t, t+ τ)τ

so that these terms in the left-hand side cancel. Similarly, multiplying and dividing by τ the fourth term inthe left-had side can be re-expressed as

Xc∼p(t, t+ τ)

φ∼p

τ

τ=ϕc∼p(t, t+ τ)

φ∼p(t, t+ τ)τ

54

Now multiply and divide by τ the first and second terms of the right-hand side, to obtain:

[vp(t+ τ)− vp(t)]− ∆Tc∼p

ϕc∼p(t, t+ τ)

φ∼p(t, t+ τ)τ =

∆Sspφp(t, t+ τ)τ −∆S

s∼pφ∼p(t, t+ τ)τ + ωp(t, t+ τ) (A.8)

where ωp(t, t+ τ) ≡ εp(t, t+ τ) + ∆Tcpξp(t, t+ τ). Crucially, notice that the error term in this equation does

not depend on τ . The left-hand side term in equation (A.8) is defined in Proposition 3 as p(t, t+τ). Becauseequation (A.8) depends on the same slope parameters and observables for both parties, it is convenient tosubtract the equation for candidate D from the equation for candidate R, which directly gives the result ofthe proposition by defining ζ(t, t+ τ) ≡ (1/2)

[$D(t, t+ τ)−$R(t, t+ τ)

].

With estimates of (∆TcD,∆

TcR,∆

SsD,∆

SsR) at hand, equation (A.7) uniquely pins down the remaining two

elasticities (∆ScD,∆

ScR).

B Appendix B

News Processing

We followed several steps to process the news article texts. The data collection was conducted in Lexis Nexisand Factiva.26 Our search terms included the name of the candidate (e.g., “Alan Kenneth Smith”) as wellas common abbreviations of the names (examples include “Senator Smith”, “Al Smith”, “Al K. Smith”).We downloaded all articles which with a succesfull hit for either search criterion.27 We followed a clean-upprocedure before computing our classification scores as follows: first we removed all common English wordsfrom the article (before the words are stemmed). Then using the Porter Stemming algorithm, we stemmedthe words to their linguistic roots. The benefit of the stemming algorithm is that it allows us to reduce thewords to workable roots which eliminate differentiations due to tense or subject.

To reduce the Type-I and Type-II error in the algorithm, we then eliminated articles irrelevant to oursetting. In the first pass, after stemming the articles, we searched for candidate names (Here we looked forcomplete names, excluding any middle names or abbreviations) If the name of the candidate was mentionedin the article, we considered the article to be relevant to our data analysis. If there was no mention of thename in the article, we removed it into a secondary group over which we undertook a secondary search toprevent the unintentional removal of relevant articles.28 We found our first pass categorizes about 25% ofthe articles as irrelevant. To reduce the potential for Type-II errors, we conducted a second manual searchon the articles that failed the first pass. A research assistant investigated the common reasons for error onarticles where a mistake arose, by looking at 10% of all removed articles. We then updated our algorithmto account for these common errors. This second pass reduced the percent of articles removed to 20%.

We carried out our search algorithm for the common words on the set of articles that passed our secondtest. For each set of candidate articles, after removal of common English words, punctuation, and stemming,we sought for the most commonly used two-word and three-word phrases. Single words may result in a highnumber of uninformative words and therefore they were not preferred for analysis here (see Gentzkow andShapiro (2010) for another example of a similar choice).

26Due to the limits of search and downloads imposed on us by Factiva, we could not rely exclusively onthis database.

27The article texts themselves are proprietary of these two companies.28For example, a common failure reason in the first pass is a mis-typed character or string (e.g., instead

of “Senator Elizabeth”, the article would be stored in the newspaper database as “SenatorElizabeth”. Themissing character can prevent our algorithm from picking up the name of the candidate.

55

Dropped Senate Races

Candidate Died Non-bipartisanRaces

3-way Races UnopposedRaces

UnopposedRace (inpractice)

Other Reason

MN 2002 LA 1990 AK 2010 ID 2004 VA 1990 NE 1988VT 2006 LA 1992 SD 2010 AZ 2000 IN 1990VT 2012 LA 2002 AR 1990 MA 2002 ND 1992

CT 2006 GA 1990 MS 2002 TN 1994FL 2010 MS 1990 VA 2002 KS 1996ME 2012 KS 2002 IN 2006 GA 2000

AR 2008 MO 2002WY 2008CO 2010DE 2010LA 2010WV 2010

Table 12: Dropped Senate Races.

Dropped Senate Races

We drop from our analysis some senate races either because they were 3-way races, unopposed races, inpractice unopposed races (more than one candidate ran but other candidates were from third parties), notbipartisan races (not a Democrat and a Republican running against each other), or because a candidate diedduring the race. Table 12 presents a list of races for which data was available, but which we excluded fromthe analysis for the aforementioned reasons.

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